2010 Fiscal Year Final Research Report
Studies on geometric properties and realization problems of invariants for classical knots and virtual knots
| Project/Area Number |
20740047
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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 | Osaka Electro-Communication University |
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Principal Investigator |
NAKAMURA Takuji Osaka Electro-Communication University, 工学部, 准教授 (60382024)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 結び目 / Alexander多項式 / ファイバー結び目 / C_n変形 / 仮想結び目 / Miyazawa多項式 / シャープ変形 |
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| Research Abstract |
In this studies, we obtain several results about realizations for geometric or algebraic properties of knots and related topics from a view of local moves for knots. In fact, we construct p-periodic knots with C_n unknotting number one for any period p. We also construct composite knots with # unknotting number one. Moreover, we obtain some partial answers for a realization problem of Alexander polynomials for # unknotting number one knots. On the other hand, we construct non-classical virtual knots with the trivial Miyazawa polynomial, which is a generalization of Jones polynomial.
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