| 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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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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 / トポロジー / 局所変形 / シャープ型結び目解消数 / 合成結び目 / Jones多項式 / 周期的結び目 |
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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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