2015 Fiscal Year Final Research Report
Quandle theory and its applicaitons for surface-links
| Project/Area Number |
25800052
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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 | Sophia University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | カンドル / 絡み目 / 曲面絡み目 / 捩れカンドル |
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| Outline of Final Research Achievements |
We studied about quandles and some generalization of quandles, and gave some application for links, surface-links and handlebody-links as below. For constructions of surface-links, we could not succeed in introducing new method of constructions.
1. For some Alexander quandle, we showed that the colorings of a knot are corresponnding to the homoomorphisms from the fundamental group of some finite cover of the 3-dimensional space branched over the knot to an abelian group. 2. We introduced the notion of a twisted quandle, and gave some generalization of the twisted Alexander invariants and simplification of the calcutation. (joint with Atsushi Ishii) 3. We showed that rack colorings are invariants for 2-dimensional knots. (joint with Kokoro Tanaka)
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| Free Research Field |
結び目理論, カンドル代数
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