2005 Fiscal Year Final Research Report Summary
A study on foliations, contactstrucures, and symplectic styructures on 3 and 4 dimensional manifolds
| Project/Area Number |
16540080
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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)
TAKAKURA Tatsuru Chuo University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (30268974)
MATSUMOTO Shigenori Nihon University, Faculty of Science and Technology, Professor, 理工学部, 教授 (80060143)
TSUBOI Takashi University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (40114566)
ONO Kaoru Hokkaido University, Graduate School Science, Professor, 大学院・理学研究科, 教授 (20204232)
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| Project Period (FY) |
2004 – 2005
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| Keywords | foliation / contact structure / Anosov flow / Stein filling / spinnable structure / symplectic structure / Reeb vector field / Hamiltonian dynamical system |
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| Research Abstract |
The head Mitsumatsu and an investigator Miyoshi colaborated with others to study the euler class of tangent bundles to foliations and (so called Thurston-Winkelnkemper's) contact structures which are associate with spinnable structures, as a typical class of convergences of contact structures to foliations. Especially they studied the (non-)vanishing of the euler class and the violation of Thurston's inequality and Bennequin's inequlity, from the topological view point of monodromies. As a consequence, a certain class of mapping classes of a surface with boundary can be presented neither as a product of only right-handed Dehn twists nor as that of only right-handed ones. This result was presented in several symposiums including the annual meeting of MSJ in March 2006 as a special invited talk by Miyoshi. The paper is under submission.
The investigator Ono studied the symplectec homology from Floer theory as well as from Seiberg-Witten theory. Including the solution to the Flux conjecture as well as the detemination of the symplectic filling of the link of simple singularities, his contributions to this area are profound.
The investigator Tsuboi studied the relationship between foliation theory and that of contact structures from the view point of the group of contact diffeomorphisms. The investigator Matsumoto stepped further to the foliation theory and studied the ends of Lie foliations.
The head investigator also studied the incompressible fluid dynamics in the framework of the geometry of volume preserving diffeomorphisms and infinite dimensional Hamiltonian systems. He proved that looking from the point of view of such global differential geometry is still valid even to viscous fluides with dissipations. This study is presented in many symposiums, especially as a special project talk in the annual meeting of MSJ in September 2005.
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Research Products
(9 results)
