| Project/Area Number |
22740048
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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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) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 結び目 / 結び目群 / character variety / Chebyshev 多項式 / trace-free 表現 / 指標多様体 / trace-free表現 / Chebyshev多項式 / knot contact homology / SL(2,C)表現 / 指標代数多様体 / 2重分岐被覆 / SL_2(C)表現 / partial order / Chebyshev polynomial |
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| Research Abstract |
This study is concerned with researches on representation theoretic structures of unknot detectors. In particular, we focus on the geometric structures on the algebraic subset S0(K) of the character variety X(K) defined by trace-free condition. In the researches, we found a family of polynomials whose zero-locus gives the set S0(K). Applying the polynomials, we found a filtration of S0(K) each of whose filters gives a knot invariant. This fact reveals a relationship between S0(K) and the abelian knot contact homology. The methods used in these researches can be also applied to determine some minimal elements for a partial ordering of prime knots.
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