Updated on 2024/02/02

写真a

 
MIYOSHI Shigeaki
 
Organization
Faculty of Science and Engineering Professor
Other responsible organization
Mathematics Course of Graduate School of Science and Engineering, Master's Program
Mathematics Course of Graduate School of Science and Engineering, Doctoral Program
Contact information
The inquiry by e-mail is 《here
External link

Degree

  • 理学博士 ( 早稲田大学 )

Research History

  • 2001.4 -  

    中央大学理工学部教授

  • 2001.4 -  

    ~ 中央大学理工学部教授

  • 1997.4 - 2001.3

    駒澤大学文学部教授   Faculty of Letters

  • 1991.4 - 1997.3

    駒澤大学文学部助教授   Faculty of Letters

  • 1989.4 - 1991.3

    駒澤大学文学部専任講師   Faculty of Letters

  • 1986.4 - 1989.3

    早稲田大学理工学部研究所奨励研究生   School of Science and Engineering

  • 1983.4 - 1986.3

    早稲田大学理工学部助手   School of Science and Engineering

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Professional Memberships

  • 日本数学会

  • American Mathematical Society

  • American Mathematical Society

Research Interests

  • Topology

Research Areas

  • Natural Science / Geometry  / 幾何学

MISC

  • Links and submersions to the plane on an open 3-manifold

    Shigeaki Miyoshi

    JOURNAL OF TOPOLOGY AND ANALYSIS   8 ( 4 )   677 - 690   2016.12

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    Language:English   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    We study the realization problem which asks if a given oriented link in an open 3-manifold can be realized as a fiber of a submersion to the Euclidean plane. We correct the results obtained before by the author which contains an error and certain imperfection, and investigate a necessary and sufficient condition for the realization in the words of well-known invariants. We obtain the condition expressed by the first homology group with mod 2 coefficient.

    DOI: 10.1142/S1793525316500266

    Web of Science

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  • Reeb components and Thurston's inequality

    Shigeaki Miyoshi, Atsuhide Mori

    FOLIATIONS, GEOMETRY, AND TOPOLOGY: PAUL SCHWEITZER FESTSCHRIFT   498   195 - +   2009

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    Language:English   Publisher:AMER MATHEMATICAL SOC  

    A foliation without Reeb components satisfies Thurston's inequality. We began to study on foliations with Reeb components which satisfy the inequality and also on those which violate it in the preceding paper.
    In this paper, we show that with finitely many exceptions all Dehn surgeries on the unique Reeb component of a certain foliation yield foliations each of which satisfies Thurston's inequality non-trivially.

    Web of Science

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  • On Thurston's inequality for spinnable foliations

    Hiroki Kodama, Yoshihiko Mitsumatsu, Shigeaki Miyoshi, Atsuhide Mori

    FOLIATIONS, GEOMETRY, AND TOPOLOGY: PAUL SCHWEITZER FESTSCHRIFT   498   173 - +   2009

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    Language:English   Publisher:AMER MATHEMATICAL SOC  

    Web of Science

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  • Reeb components and Thurston's inequality

    Foliations, Topology and Geometry in Rio, On the occasion of the 70th birthday of Paul Alexander Schweitzer   2007

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  • On representability of the smooth Euler class

    S Miyoshi

    TOHOKU MATHEMATICAL JOURNAL   56 ( 4 )   523 - 530   2004.12

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    Language:English   Publisher:TOHOKU UNIVERSITY  

    The Eater class, which lies in the second cohomology of the group of orientation preserving homeomorphisms of the circle, is pulled back to the "smooth" Euler class if) the cohomology of the group of orientation preserving smooth diffeornorphisms of the circle. Suppose a surface group Gamma (of genus > 1) is a normal subgroup of a group G, so that we have an extension of Q = G/Gamma by Gamma . We prove that if the canonical outer action of Q on Gamma is finite, then there is a canonical second cohomology class of G restricting to the Euler class on Gamma which is smoothly representable, that is, it is pulled back from the smooth Euler class by a representation from G to the group of diffeomorphisms. Also, we prove that if the above outer action is infinite, then any second cohomology class of G restricting to the Euler class on Gamma is not smoothly representable.

    DOI: 10.2748/tmj/1113246748

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  • On representability of the smooth euler class

    Shigeaki Miyoshi

    Tohoku Mathematical Journal   56 ( 4 )   523 - 530   2004

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    The Euler class, which lies in the second cohomology of the group of orientation preserving homeomorphisms of the circle, is pulled back to the “smooth” Euler class in the cohomology of the group of orientation preserving smooth diffeomorphisms of the circle. Suppose a surface group Γ (of genus &gt
    1) is a normal subgroup of a group G, so that we have an extension of Q = G/Γ by Γ. We prove that if the canonical outer action of Q on Γ is finite, then there is a canonical second cohomology class of G restricting to the Euler class on Γ which is smoothly representable, that is, it is pulled back from the smooth Euler class by a representation from G to the group of diffeomorphisms. Also, we prove that if the above outer action is infinite, then any second cohomology class of G restricting to the Euler class on Γ is not smoothly representable. © 2004 Euclid. All rights reserved.

    DOI: 10.2748/tmj/1113246748

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  • Some remarks on the Euler class of a spinnable foliation

    Geometry and Foliations Kyoto 2003, International Conference held at Ryukyu University, September 10-19, 2003   2003

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  • A cyclic cocycle associated with Euler cocycle

    Aspect of Foliation Theory in Geometry, Topology and Physics, July 15-November 30, 2002   2002

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  • A remark on torsion Euler classes of circle bundles Reviewed

    Shigeaki Miyoshi

    Tokyo Journal of Mathematics   24 ( 1 )   189 - 194   2001.6

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    Language:English   Publisher:kinokuniya  

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  • A remark on torsion euler classes of circle bundles

    Shigeaki Miyoshi

    Tokyo Journal of Mathematics   24 ( 1 )   189 - 194   2001

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    We show that any torsion class e ∈ H2(M
    Z) of any closed manifold M is realized as the Euler class of a smoothly foliated orientable circle bundle over M . In the case where M is a 3-manifold, we construct the homomorphism (math equation) explicitly whose Euler class is the given torsion class. © 2001 by the University of Notre Dame. All rights reserved.

    DOI: 10.3836/tjm/1255958322

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  • Euler classes and foliated circle bundles

    “Foliations and Geometry 2001”, August 2nd to 11th, 2001   2001

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  • On representability of the smooth Euler class

    1998

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  • On foliated circle bundles over closed orientable 3-manifolds

    Shigeaki Miyoshi

    Commentarii Mathematici Helvetici   72 ( 3 )   400 - 410   1997

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    Language:English   Publisher:Birkhauser Verlag Basel  

    We show that there exists a family of smooth orientable circle bundles over closed orientable 3-manifolds each of which has a codimension-one foliation transverse to the fibres of class C0 but has none of class C3. There arises a necessary condition induced from the Milnor-Wood inequality for the existence of a foliation transverse to the fibres of an orientable circle bundle over a closed orientable 3-manifold. We show that with some exceptions this necessary condition is also sufficient for the existence of a smooth transverse foliation if the base space is a closed Seifert fibred manifold.

    DOI: 10.1007/s000140050024

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  • On foliated circle bundles over closed orientable 3-manifolds

    S Miyoshi

    COMMENTARII MATHEMATICI HELVETICI   72 ( 3 )   400 - 410   1997

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    We show that there exists a family of smooth orientable circle bundles over closed orientable 3-manifolds each of which has a codimension-one foliation transverse to the fibres of class C-0 but has none of class C-3. There arises a necessary condition induced from the Milnor-Wood inequality for the existence of a foliation transverse to the fibres of an orientable circle bundle over a closed orientable 8-manifold. We show that with some exceptions this necessary condition is also sufficient for the existence of a, smooth transverse foliation if the base space is a closed Seifert fibred manifold.

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  • C^{\infty} Reeb links have all Alexander polynomials

    Shigeaki Miyoshi

    J. of the Faculty of Letters   54   29 - 32   1996.3

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    Language:English   Publishing type:Article, review, commentary, editorial, etc. (other)   Publisher:Komazawa University  

    CiNii Books

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  • C¹ºº Reeb links have all Alexander polynomials

    J. of the Faculty of Letters   54   29 - 32   1996

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  • LINKS AND GLOBALLY COMPLETELY INTEGRABLE VECTOR-FIELDS ON AN OPEN 3-MANIFOLD

    S MIYOSHI

    TOPOLOGY   34 ( 2 )   383 - 387   1995.4

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    Language:English   Publisher:PERGAMON-ELSEVIER SCIENCE LTD  

    FOR AN ORIENTED LINK L is an open oriented 3-manifold M, we give a necessary and sufficient condition for the existence of a submersion phi:M --> R(2) whose preimage phi(-1)(0) is L. Also, we prove there always exists a submersion psi:M --> R(2) such that the union of the compact components of the preimage psi(-1)(0) is L for any link L in M.

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  • Links and globally completely integrable vector field on an open 3-manifold Reviewed

    Shigeaki Miyoshi

    Topology   34 ( 2 )   383 - 387   1995.4

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    Language:English   Publisher:Pergamon Press  

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  • On foliated circle bundles over 3-manifolds

    1995

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  • On concordance between codimension-one foliations

    Shigeaki Miyoshi

    J. of the Faculty of Letters   48   141 - 157   1990.3

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    Language:English   Publishing type:Article, review, commentary, editorial, etc. (other)   Publisher:Komazawa University  

    CiNii Books

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  • On concordance between codimension-one foliations

    Shigeaki Miyoshi

    J. of the Faculty of Letters   48   141 - 157   1990.3

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  • On Sullivan's vanishing cycles in codimension-one foliations Reviewed

    Shigeaki Miyoshi

    Tokyo J. of Mathematics   11 ( 2 )   387 - 404   1988.12

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    Language:English   Publisher:Kinokuniya  

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  • On Sullivan’s vanishing cycles in codimension-one foliations

    Shigeaki Miyoshi

    Tokyo Journal of Mathematics   11 ( 2 )   387 - 404   1988

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  • Existence of Sullivan's vanishing cycles in codimension-one foliations

    Shigeaki Miyoshi

    Topology and Computer Science   395 - 406   1987.6

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  • Existence of Sullivan's vanishing cycles in codimension-one foliations Reviewed

    Shigeaki Miyoshi

    Topology and Computer Science   395 - 406   1987.6

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    Language:English   Publisher:Kinokuniya  

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  • On the placement problem of Reeb components

    Shigeaki Miyoshi

    Commentarii Mathematici Helvetici   57 ( 1 )   260 - 281   1982.12

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    Language:English   Publisher:Birkhäuser-Verlag  

    DOI: 10.1007/BF02565861

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  • Foliated round surgery of codimension-one foliated manifolds

    Shigeaki Miyoshi

    Topology   21 ( 3 )   245 - 261   1982

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  • ON THE PLACEMENT PROBLEM OF REEB COMPONENTS

    S MIYOSHI

    COMMENTARII MATHEMATICI HELVETICI   57 ( 2 )   260 - 281   1982

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    Language:English   Publisher:BIRKHAUSER VERLAG AG  

    Web of Science

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  • Foliated round surgery of codimension-one foliated manifolds

    Shigeaki Miyoshi

    Topology   21 ( 3 )   245 - 265   1982

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Presentations

  • Construction of smooth typical foliations of 3-manifolds

    Shigeaki Miyoshi

    Foliations and diffeomorphism groups 2018  ( Tambara Institute of Mathematical Sciences, University of Tokyo )   2018.10  Professor Takashi Tsuboi Graduate School of Mathematical Sciences, University of Tokyo

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    Language:English   Presentation type:Oral presentation (general)  

    We show the construction of a smooth codimension-one typical foliation on every orientable closed 3-manifold.

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  • On a knotted closed orbit of a completely integrable vector field

    Contact structures, singularities, differential equations and their related topics  2016.1 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Knots and submersions to the plane on an open 3-manifold

    Geometry Seminar, Instituto de Ciencias Matematicas  2015.3 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • On a construction realizing a knot as a fibre of a submersion to the plane

    Seminar Tohoku knots 2013, Tohoku University  2013.10 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Links and submersions to the plane on an open 3-manifold

    59th Topology Symposium, Mathematical Society of Japan, at Saga University  2012.8 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Links and submersions on an open 3-manifold

    Plane fields on manifolds and diffeomorphism groups 2011, University of Tokyo Tambara International Seminar House  2011.10 

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  • A construction of a typical foliation on a 3-manifold

    Foliations and groups of diffeomorphisms 2010, University of Tokyo Tambara International Seminar House  2010.10 

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  • A construction of a typical foliation on a 3-manifold

    Geometry and Topology of foliations, Centre de Recerca Matematica at Barcelona, Spain  2010.7 

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  • On Thurston's inequality for foliations 3

    joint work with, Hiroki Kodama, Yoshihiko Mitsumatsu, Atsuhide Mori

    Foliations theory symposium, University of Tokyo Tambara International Seminar House  2007.10 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Reeb components and Thurston's inequality

    joint work with, Atsuhide Mori

    Foliations, Topology and Geometry in Rio, On the occasion of the 70th birthday of Paul Alexander Schweitzer/Pontificia Universidade Catolica do Rio de Janeiro  2007.8 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • 葉層構造に対する Thurston の不等式

    日本数学会 2006 年度年会,日本数学会,於中央大学理工学部  2006.3 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Thurston の不等式と回転可能葉層構造について

    児玉大樹, 三松佳彦, 森淳秀との共同研究

    研究集会「Intelligence of Low Dimensional Topology」(21世紀 COE プログラム「結び目を焦点とする広角度の数学拠点の形成」(拠点リーダー河内明夫))  2005.11 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Reeb components and Thurston's inequality

    森淳秀との共同研究

    研究集会「葉層構造とその周辺」日本学術振興会科学研究費,基盤研究(A)「多様体の無限変換群の総合的研究」(課題番号 16204004, 代表者 坪井 俊)  2005.10 

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  • 回転可能葉層構造に対する Thurston の不等式について II

    児玉大樹, 三松佳彦, 森淳秀との共同研究

    研究集会「葉層構造とその周辺」日本学術振興会科学研究費,基盤研究(A)(代表者 坪井 俊)および基盤研究(C)(代表者 三松佳彦  2004.10 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • 回転可能葉層と Thurston の不等式について

    児玉大樹, 三松佳彦, 森淳秀との共同研究

    シンポジウム「接触構造,特異点と周辺分野」科学研究費基盤研究A(1)課題番号15204002「特異点からみた様々な幾何学の研究」(代表 泉屋周一)及び基盤研究A(1)課題番号15204004「3 次元多様体とトポロジーII」(代表 小島定  2004.1 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Some remarks on the Euler class of a spinnable foliation

    joint work with, Hiroki Kodama, Yoshihiko Mitsumatsu, Atsuhide Mori

    Geometry and Foliations Kyoto 2003,International Conference held at Ryukyu University,September 10-19, 2003  2003.9 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • A cyclic cocycle associated with Euler cocycle

    Aspect of Foliation Theory in Geometry, Topology and Physics, July 15-November 30, 2002/Erwin Schrodinger International Institute for Mathematical Physics Vienna, Austria  2002.8 

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    Language:English   Presentation type:Oral presentation (general)  

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  • Euler classes and foliated circle bundles

    Foliations and Geometry 2001, August 2nd to 11th, 2001/at PUC-Rio, Rio de Janeiro, Brazil  2001.8 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • 滑らかなEuler類の表現可能性について

    日本数学科1999年度秋季総合分科会トポロジー分科会アブストラクト,日本数学会  1999.9 

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  • On representability of the smooth Euler class

    葉層構造の総合的研究,基盤研究 (B)「葉層構造と力学系の総合的研究」(課題番号 80060143 研究代表者 松元重則)による研究集会  1998.11 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • 捩れEuler類と葉層円周束について

    日本数学会1997年度秋季総合分科会トポロジー分科会アブストラクト,日本数学会  1997.9 

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  • On foliated circle bundles over 3-manifolds

    葉層構造の幾何学,研究集会(平成7年度科学研究費総合 A)  1995.11 

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  • 2,3次元多様体上の葉層S1束について

    第42回トポロジーシンポジウム,日本数学会,於弘前大学  1995.7 

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  • Links and simple foliations

    葉層構造と大域幾何学,研究集会(平成6年度科学研究費総合 A)  1994.10 

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    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Links and submersions

    日本数学会1994年度秋季総合分科会トポロジー分科会アブストラクト,日本数学会  1994.9 

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  • S^{3} の余次元1葉層構造についてのいくつかの注意

    日本数学会1981年度秋季総合分科会トポロジー分科会アブストラクト,日本数学会  1981.10 

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  • 余次元1葉層構造の葉層円形手術

    日本数学会1981年度秋季総合分科会トポロジー分科会アブストラクト,日本数学会  1981.10 

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Works

  • Organaizer of the international conference Geometry and Foliations 2013

    2013.9    

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  • Organaizer of the international conference BGamma School

    2013.9    

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  • 国際会議 "BGamma School" 組織委員

    2013.9 -  

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  • 国際会議 "Geometry and Foliations 2013" 組織委員

    2013.9 -  

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  • 3次元開多様体の絡み目と R^2 への沈め込みに関する研究

    2012.4 -  

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  • 葉層構造に対する Thurston の不等式と接触トポロジーに関する研究

    2011.4 -  

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  • シンプレクティック商の大域的構造と不変量の研究

    2009.4 -  

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  • 葉層構造に対する Thurston の不等式に関する研究

    2008.4 -  

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  • A reserch on a foliation, a contact structure and Euler class

    2006 - 2008

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  • On Thurston's inequality

    2006 - 2008

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  • Thurston の不等式に関する研究

    2006.4 -  

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  • 葉層構造と接触構造の微分位相的研究

    2006.4 -  

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  • 葉層構造,接触構造と Euler 類に関する研究

    2006.4 -  

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  • シンプレクティック空間の幾何と種々の不変量の研究

    2005.4 -  

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  • 3・4次元多様体上の葉層・接触・シンプレクティック構造の研究

    2004.4 -  

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  • シンプレクティック空間の不変量とその表現論的構造の研究

    2003.4 -  

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  • 情報幾何を利用したアファイン空間内の微分幾何学的アファイン超曲面に関する研究

    2003.4 -  

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  • 絡み目とグラフの不変量の計算アルゴリズムに関する研究

    2002.4 -  

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  • 3・4次元多様体上の接触構造と葉層構造の研究

    2001.4 -  

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Research Projects

  • 力学的微分トポロジーによる葉層・接触・シンプレクティック構造の研究

    Grant number:21H00985  2021.4 - 2026.3

    日本学術振興会  科学研究費助成事業  基盤研究(B)  中央大学

    三松 佳彦, 直江 央寛, 高倉 樹, 太田 啓史, 三好 重明, 粕谷 直彦

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    Grant amount: \10270000 ( Direct Cost: \7900000 、 Indirect Cost: \2370000 )

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  • Study on symplectic quotients concerned with branching problems

    Grant number:16K05137  2016.4 - 2020.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Chuo University

    Takakura Tatsuru

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    Grant amount: \2860000 ( Direct Cost: \2200000 、 Indirect Cost: \660000 )

    We studied the multiplicity varieties and multiple weight varieties associated with coadjoint orbits (flag manifolds) of a compact Lie group, and obtained the results as follows.
    First, we characterized the special vector volume function of type A, by means of a system of differential equations (arXiv: 1904.05000). Second, we proved that the symplectic volume function of a nondegenerate multiple weight variety of type A determines the cohomology ring over real numbers, and applied it to the study of double weight varieties of type A2. Third, we showed that a nondegenerate special weight variety of type A has the structure of a generalized Bott tower.
    We gave presentations about the results as above in some international and domestic conferences.

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  • Study of invariants and various structure of symplectic quotients

    Grant number:24540093  2012.4 - 2015.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Chuo University

    TAKAKURA TATSURU, MIYOSHI Shigeaki

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    Grant amount: \4030000 ( Direct Cost: \3100000 、 Indirect Cost: \930000 )

    First, we obtained an explicit formula for a vector partition function with possibly negative weights. As an example, for the root system of type A, we obtain an alternative proof of certain formulas for the vector partition/volume function over the `nice chamber.' They are also applied to a presentation of solutions of a certain hypergeometric system. Second, we explicitly described the special multiple weight variety of type A as a tower of projective space bundles. Consequently, the cohomology ring of this space is written down in a very simple form. As an application, we obtained a system of differential equations which characterizes the special vector volume function of type A.

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  • A research on links and submersions to R^2 on an open 3-manifold

    2012.4 - 2014.3

    三好 重明

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    Grant type:Competitive

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  • Topological study of foliations and contact structures

    Grant number:22340015  2010.10 - 2014.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Chuo University

    MITSUMATSU Yoshihiko, MIYOSHI Shigeaki, TAKAKURA Tatsuru, MATSUMOTO Shigenori, TSUBOI Takashi, KIMURA Yoshifumi, MORIYOSHI Hitoshi, OHTA Hiroshi

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    Grant amount: \8710000 ( Direct Cost: \6700000 、 Indirect Cost: \2010000 )

    Foliations and contact structures are studied, with a focus on those structures on 3, 4, and 5 dimensional spaces. Especially the construction of important examples and their mutual relationships are investigated. Interactions of many mathematical theories such as Milnor fibrations associated with singularities, fluid mechanics, symplectic geometry which is a refinement of classical mechanics, and several complex variables, re flected on those structures and objects are studied.
    This study is also understood as looking at the tightness of those structures which is interpreted as the result of such mathematical theories are reflected on the geodesic flows of surfaces, which gives rise to a special class of flows called `Anosov flows'.

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  • A ressearch on the global structure of a symplectic quotient and its invariant

    2009.4 - 2012.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    高倉 樹

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  • A research on Thurston's inequality for foliations

    Grant number:20540091  2008.4 - 2011.3

    文部科学省  科学研究費補助金 基盤研究(C)  Grant-in-Aid for Scientific Research (C)  Chuo University

    三好 重明

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    Grant type:Competitive

    Grant amount: \2860000 ( Direct Cost: \2200000 、 Indirect Cost: \660000 )

    It was only known that Reebless foliations among codimension-one foliations on a 3-manifold satisfy Thurston's inequality. Also, according to the latest research the condition of Reebless is known not to be necessary for Thurston's inequality. Moreover, the example not satisfying Thurston's inequality had not been known. In this research, we studied spinnable foliations in detail and obtained a sufficient condition for spinnable foliations. Thus we constructed a family of spinnable foliations each of which satisfies Thurston's inequality and an example of the foliation not satisfying Thurston's inequality.

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  • A differential topological research on foliations and contact structures

    2006.4 - 2009.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(B) 

    三松 佳彦

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  • On Thurstons inequality

    2006.4 - 2008.3

    中央大学  中央大学特定課題研究費 

    三好 重明

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    Grant type:Competitive

    Grant amount: \1200000

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  • "A reserch on a foliation, a contact structure and Euler class"

    Grant number:18540095  2006.4 - 2008.3

    文部科学省  科学研究費補助金 基盤研究(C)  Grant-in-Aid for Scientific Research (C)  Chuo University

    三好 重明

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    Grant type:Competitive

    Grant amount: \2100000 ( Direct Cost: \2100000 、 Indirect Cost: \240000 )

    W. Thurston showed that a foliation on a 3-manifold which has no Reeb component enjoys the property that the Euler class of the tangent bundle satisfies an inequality, Thurston's inequality. On the other hand, the Reeb foliation on the three sphere satisfies Thurston's inequality and a previous research followed by this research showed that there is a class of foliations each of which has Reeb components and satisfi es Thurston's inequality.
    In the research in 2006, for a class of foliations which are called spinnable foliations, we obtained a sufficient condition for the foliation satisfying Thurston's inequality. Moreover, we revealed an aspect where Thurston's inequality does not hold. They are described by properties of the monodromy diffeomorphisms which determine the spinnable foliations
    In view of the research with respect to the convergence of contact structures to foliations, we studied a finer inequality, the relative version of Thurston's inequality, which deepens the research until 2006. In fact, for spinnable foliations we showed that the relative version implies the absolute version. The same statement for contact structures was known however, it does not hold in general for foliations. Also in 2007, we found the method to construct a foliation which satisfies Thurston's inequality with Euler class of infinite order. Until then, all foliations which satisfies Thurston's inequality have trivial Euler class. Indeed, we can find'a spinnable foliation whose Euler class is of infinite order by the research in 2006. Then we can perform Dehn surgery along the Reeb component and with certain condition on the original spinnable foliation we can conclude that with finitely many exceptions the resultant satisfies Thurston's inequality with Euler class of infinite order by virtue of D. Gabai's sutured manifold theory.

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  • 葉層構造の位相幾何学についての研究

    2008 -  

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    Grant type:Competitive

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  • A research on the geometry of symplectic spaces and various invariants

    2005.4 - 2007.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    高倉 樹

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  • "A research on foliations, contact structures and symplectic structures on 3 and 4 dimensional manifolds"

    2004.4 - 2006.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    三松 佳彦

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  • A research on differential geometric affine hypersurfaces in an affine spaces using information geometry

    2003.4 - 2006.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    松山 善男

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    Grant type:Competitive

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  • A research on the invariants of symplectic spaces and their structures in the representation theory

    2003.4 - 2005.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    高倉 樹

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    Grant type:Competitive

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  • A research on the algorithms of the invariants of links and graphs

    2002.4 - 2005.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    山本 慎

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  • A research on contact structures and foliations on 3 and 4 dimensional manifolds

    2001.4 - 2004.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(B) 

    三松 佳彦

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