2009 Fiscal Year Final Research Report
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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| Keywords | トポロジー / 幾何学 |
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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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