Cobordism category of 3-manifolds and analysis on moduli spaces of flat connections
| Project/Area Number |
26400101
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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 | Ritsumeikan University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ゲージ理論 / 負定値同境 / 平坦接続 / インスタントン / レンズ空間 / ホモロジー同境群 / チャーン・サイモンズ不変量 / 有理ホモロジー球面 / Chern-Simons不変量 / 指標多様体 / モジュライ空間 / 結び目 / 指数定理 |
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| Outline of Final Research Achievements |
The cobordism relations regarding several 3 dimensional manifolds as boundary components of a 4 dimensional manifold is one of the important object to study on the fundamental building block of 4 dimensional manifolds. In this research, we investigated the moduli spaces of flat connections over 4 dimensional manifolds to study cobordism relations. In particular, for cobordisms among 3 dimensional manifolds called lens spaces which have negative definite intersection forms, we have shown a generation of certain pair of lens spaces in the cobordism. By using this result, we clarify a certain structure of the homology cobordism group of homology 3 spheres.
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Report
(4 results)
Research Products
(9 results)
