2009 Fiscal Year Final Research Report
Study on knot invariants detecting the unknot
| 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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| Keywords | 結び目 / 結び目群 / character variety / Chebyshev多項式 |
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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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