Chern-Simons perturbation theory and its application to topology
| Project/Area Number |
17K05252
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University (2021-2022)
Shimane University (2017-2020) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 微分同相群 / 配置空間 / グラフホモロジー / 4次元多様体 / 有限型不変量 / Morse理論 / ホモトピー群 / 可微分多様体 / 配置空間積分 / グラフクラスパー / 微分同相 / Chern-Simons摂動理論 / 局所系 / クラスパー / 有理ホモトピー群 / Kontsevich特性類 / 擬アイソトピー / 埋め込み / Morseホモトピー / 幾何学 |
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| Outline of Final Research Achievements |
Kontsevich constructed differential topological invariants of 3-manifolds and families of homology disks by configuration space integrals. We studied Kontsevich's invariants and their applications to topology, and obtained the following results.
(1) We proved that the group of relative diffeomorphisms of the 4-dimensional disk is not contractible, by using Kontsevich's configuration space integral invariant.
(2) We extended Kontsevich's configuration space integral invariant to some closed 4-manifolds equipped with non-trivial local coefficient systems. By using the extension, we found many non-trivial elements of the mapping class groups of some closed 4-manifolds.
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| Academic Significance and Societal Importance of the Research Achievements |
4次元円板の相対微分同相の群のトポロジーは、多様体の局所構造に関するカテゴリーの差の根本に関わる基本的な研究対象であるが、その具体的な構造についてはほとんど何もわかっていない状態であった。そのホモトピー型が全く自明でないということを初めて明らかにしたことは学術的意義があると考える。
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Report
(7 results)
Research Products
(26 results)
