| Project/Area Number |
20840038
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| Research Category |
Grant-in-Aid for Young Scientists (Start-up)
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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 |
NAGASATO Fumikazu Meijo University, 理工学部, 助教 (30513634)
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| Project Period (FY) |
2008 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥2,496,000 (Direct Cost: ¥1,920,000、Indirect Cost: ¥576,000)
Fiscal Year 2009: ¥1,066,000 (Direct Cost: ¥820,000、Indirect Cost: ¥246,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 結び目 / 結び目群 / character variety / Chebyshev多項式 / SL_2(C)表現 / metabelian representation / partial order / chebyshev polynomial / SL_2(C)-表現 / Character variety / メタベリアン表現 / Khovanov homology / Casson-Lin不変量 / 2橋結び目 |
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| Research Abstract |
This study is concerned with a research on the structure of knot invariants (possibly) detecting the unknot. More precisely, we focus on the geometric structure of the character variety X(K), which is defined by the zeros of some algebraic polynomials associated with a knot K. In fact, we found that the section (subvariety) S(K) of X(K) defined by a special equation can detect the unknot in the set of small knots. This result can give some applications to the knot theory.
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