A study on knots and transverse knots using braid theory and Floer theory
| Project/Area Number |
23740053
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 横断的結び目 / 組み紐 / フレアーホモロジー群 / 2橋指数 |
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| Research Abstract |
I constructed an example of a pair of closed 4-braids with the following properties; (1) they are related by a Hopf-flype, (2) they are distinct as transverse knots, (3) they have the same self-linking number. I also constructed a similar example of a pair of a closed 3-braid and a closed 7-braid. I determined 2-bridge numbers of torus knots of type (p, q), where p and q are integers. I also determined 2-bridge numbers of knots that had alternating diagrams of closed braids. An invariant of a mapping class group of a surface (fixing its boundary) is defined in bordered Floer theory. When a surface has one boundary component and is of genus 2, I calculated this invariant for elements in Torelli group. Torelli group is a subgroup of a mapping class group of a surface that acts trivially on its first homology group.
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Report
(4 results)
Research Products
(7 results)
