2017 Fiscal Year Final Research Report
Topological invariants of manifolds, modular forms and Dedekind symbols
| Project/Area Number |
26400098
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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 | Tsuda University |
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Principal Investigator |
Fukuhara Shinji 津田塾大学, その他部局等, 名誉教授 (20011687)
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| Co-Investigator(Kenkyū-buntansha) |
宮澤 治子 津田塾大学, 付置研究所, 研究員 (40266276)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 位相不変量 / デデキント和 / 保型形式 / 結び目 / 多様体 |
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| Outline of Final Research Achievements |
We studied generalized Dedekind symbols which are useful for expressing topological invariants. The Dedekind symbols satisfy reciprocity laws. We give general forms, not only for odd symbols, but also for even symbols.
Another result is concerned with homotopy invariants of curves on a surface. The invariant can be used for estimating numbers of self-intersections. This invariant has been inspired by Kauffman-Jones polynomials.
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| Free Research Field |
幾何学
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