2013 Fiscal Year Final Research Report
Topological study of foliations and contact structures
| Project/Area Number |
22340015
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
MIYOSHI Shigeaki 中央大学, 理工学部, 教授 (60166212)
TAKAKURA Tatsuru 中央大学, 理工学部, 准教授 (30268974)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Shigenori 日本大学, 理工学部, 教授 (80060143)
TSUBOI Takashi 東京大学, 数理科学研究科, 教授 (40114566)
KIMURA Yoshifumi 名古屋大学, 多元数理科学研究科, 教授 (70169944)
MORIYOSHI Hitoshi 名古屋大学, 多元数理科学研究科, 教授 (00239708)
OHTA Hiroshi 名古屋大学, 多元数理科学研究科, 教授 (50223839)
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| Project Period (FY) |
2010-10-20 – 2014-03-31
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| Keywords | 葉層構造 / 接触構造 / シンプレクティック構造 / Anosov 流・葉層 / 強擬凸性 / 葉向コホモロジー / ミルナー・ファイブレーション / 非圧縮流体 |
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| Research Abstract |
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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Research Products
(27 results)
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[Presentation] Secondary cyclic cocycle for Connes2013
Author(s)
MORIYOSHI Hitoshi
Organizer
Chern character on a Cantor set, China-Japan Conference on Noncommutative Geometry and K-Theory
Place of Presentation
Jilin University, Changchun, China
Year and Date
2013-06-14
Invited
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