A study on knots using braid theory and Heegaard Floer theory
| Project/Area Number |
20740041
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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 | Hiroshima University |
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Principal Investigator |
MATSUDA Hiroshi Hiroshima University, 大学院・理学研究科, 助教 (70372703)
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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 |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 組み紐 / 横断的結び目 / 組み紐群 |
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| Research Abstract |
When n=1, 2 and 3, we construct a pair of transverse knots S and T satisfying the following properties (1)-(4) ;
(1) S(n) is obtained from a transverse knot S by n stabilizations,
(2) the topological knot type of T is the same as that of S(n),
(3) the self-linking number of T is equal to that of S(n), and
(4) T is not transversely isotopic to S(n).
A topological knot type satisfying the above properties (2)-(4) is called "transversely non-simple." It was not known whether there exist transversely non-simple knot types until recently. In particular, this is the first example of a pair of transversely non-simple knots such that one of the pair admits at least two destabilizations.
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Report
(4 results)
Research Products
(19 results)
