The number of Reidemeister moves needed for connecting two link diagrams representing the same link.
| Project/Area Number |
18540100
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Japan Women's University |
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Principal Investigator |
HAYASHI Chuichiro Japan Women's University, 理学部, 准教授 (20281321)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,120,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | トポロジー / 幾何学 / 結び目理論 / ライデマイスター変形 / 絡み目射影図 / 上界 / ファンダメンタル曲面 / ノーマル曲面 / fundamental surface / lens space / non-orientable surface / triangulation / normal surface / Q-theory / vertex surface / 3-manifold / normal曲面 / fundamental曲面 / レンズ空間 / Reldemeister変形 |
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| Research Abstract |
It is well-known that any two knot diagrams which represent the same knot are connected by a finite sequence of Reidemeister moves. We show that the minimal sequence of Reidemister moves connecting the usual diagram of the (n+1, n)-torus knot and that of the (n, n+1)-torus knot contains precisely {(n-1)n(2n-1)/6}+1 Reidemeister moves.
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Report
(6 results)
Research Products
(15 results)
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[Presentation] Q-fundamental surfaces in lens spaces2007
Author(s)
Chuichiro Hayashi, Miwa Iwakura
Organizer
Knotting Mathematics and Art : Conference in Low Dimensional Topology and Mathematical Art
Place of Presentation
University of South Florida フロリダ州、アメリカ合衆国
Year and Date
2007-11-02
Related Report
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