2017 Fiscal Year Final Research Report
Morse theory and topology of manifolds / groups of diffeomorphisms
| Project/Area Number |
26800041
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Shimane University |
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Principal Investigator |
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| Research Collaborator |
SAKAI Keiichi 信州大学, 学術研究院理学系, 准教授 (20466824)
SHIMIZU Tatsuro 京都大学, 数理解析研究所, 特定助教 (00738859)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | Chern-Simons摂動理論 / Morse理論 / 有限型不変量 / ３次元多様体 / 微分同相群 / 有理ホモトピー群 |
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| Outline of Final Research Achievements |
We studied a construction of an equivariant perturbative invariant for 3-manifolds with positive first Betti number, and its relation to finite type invariants. We coustructed an equivariant perturbative invariant for 3-manifolds with positive first Betti number by using Fukaya's Morse homotopy theory. We showed that the degree k part in a filtration that defines a finite type invariant is at least the image of the natural map from the space of k-vertex trivalent graphs colored by Laurent polynomials to the space of k-vertex trivalent graphs colored by rational functions.
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| Free Research Field |
位相幾何学
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