| Project/Area Number |
13440026
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Chuo University |
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Principal Investigator |
MITSUMATSU Yoshihiko Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (70190725)
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| Co-Investigator(Kenkyū-buntansha) |
MIYOSHI Shigeaki Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60166212)
TSUBOI Takashi University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (40114566)
SATO Hajime Nagoya University, Graduate School of Mathematical Sciences, Professor, 大学院・多元数理科学研究科, 教授 (30011612)
TAKAKURA Tatsuru Chuo University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (30268974)
ONO Kaoru Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20204232)
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| Project Period (FY) |
2001 – 2003
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| Keywords | contact structures / foliations / symplectic structures / bi-contact structures / Ansov flows / foliated cohomology / asymptotic linking / Stein surface |
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| Research Abstract |
Based on the notion of asymptotic linking, the head investigator proposed the framework where the study on contact structures and that on foliations would be unified, and began the research. Op the side of foliations, it turned out that exotic classes and the 1st foliated cohomology are strongly related to this framework. On the other side, the torsion invariant of contact structures has a deep relation with it. For algebraic Anosov foliations, we also established the computation of its 1st foliated cohomology and found its relation to local orbit rigidity.
A research group including Miyoshi and Mitsumatsu investigated Thurston's inequality for foliations on the boundary of compact Stein surfaces and established the absolute version of the inequality for certain cases. The relative ersion and more general case are left for the future as important subject. Tsuboi and Mitsumatsu worked on the perfectness of groups of diffeomorphisms preservein certain geometric structures. Especially Tsuboi provednthe perfectness for contact diffeomorphisms and analytic diffeomorphisms of certain manifolds. Tsuboi also classified regular bi-contact structures on Seifert fibered spaces.
Another group including Ono and Ohta, mainly working on contact/symlectic topology, characterized the symplectic diffeo-types of the filling of the link of simple and hyper-elliptic singularities. Also they got started the construction of obstruction theory for Lagrangian Floer homology theory.
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