| Project/Area Number |
26800046
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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 | Meijo University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 結び目 / 基本群 / トレースフリー表現 / 指標多様体 / コンタクトホモロジー / ２重分岐被覆 / 幽霊指標 / 結び目群 / ノットコンタクトホモロジー / knot contact homology / character variety / ghost character / minimal element / トレースフリー断面 / 半順序 |
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| Outline of Final Research Achievements |
This project focuses on a representation theoretical mechanism relating the abelian knot contact homology and the character ring of the 2-fold branched cover of a 3-sphere branched along a knot. This relationship was conjectured by L. Ng, and it has been established by him for 2-bridge knots. In this project, we first introduced a new notion called a ghost character of a knot, which gives an obstruction for the conjecture to be true. Using it, in a joint work with Shinnosuke Suzuki, who was a graduate student at Meijo University, we found a counterexample of the conjecture for some torus knots. We are still researching this relationship to reveal the representation theoretical mechanism of the knot contact homology completely.
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