A study of cohomology of subgroups of the mapping class group and finite type invariants of homology three spheres
| Project/Area Number |
26800034
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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 | Tokyo Denki University (2015-2018)
Gifu University (2014) |
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Principal Investigator |
SATO Masatoshi 東京電機大学, 未来科学部, 准教授 (10632010)
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| Research Collaborator |
ISHIDA Tomohiko
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 写像類群 / ハンドル体 / 円板複体 / 3次元ハンドル体 / 配置空間 / Krizモデル / ハンドル体写像類群 / 有限型不変量 / Torelli群 |
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| Outline of Final Research Achievements |
We studied mainly on the cohomology group of the handlebody mapping class group. For every genus, we computed its first homology group with coefficients in the first integral homology of the boundary surface of the handlebody. This is a joint work with Tomohiko Ishida, and the results are published in Osaka Journal of Mathematics. In genus two case, we also computed the integral cohomology group of the handlebody group. In genus three case, we gave an upper bound on the rank of the rational cohomology group of the handlebody mapping class group.
We also computed values of LMO functor on some elements in the Torelli group and Johnson kernel.
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| Academic Significance and Societal Importance of the Research Achievements |
低次元トポロジーにおいて曲面の写像類群は2次元の図形の対称性を記述する重要な対象である。また、3次元のすべての図形は3次元の基本的な図形の貼りあわせとして記述されるが、その貼りあわせをつかさどるものが曲面の写像類群である。
本研究の興味は、この曲面の対称性の情報と3次元の図形の不変量の関係であり、貼り合わせを表す2次元図形の対称性という群論的対象を通して、3次元の幾何的対象の情報を記述することが目標である。本研究の1つの成果としてハンドル体写像類群のコホモロジー群という群論的対象の情報が得られた。
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Report
(6 results)
Research Products
(20 results)
