Studies on the Gordian complex and wild knots
| Project/Area Number |
22840037
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Osaka Prefecture University (2011)
Osaka City University (2010) |
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Principal Investigator |
JONG In dae 大阪府立大学, 高等教育推進機構, 教育拠点形成教員 (30587788)
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| Project Period (FY) |
2010 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥1,495,000 (Direct Cost: ¥1,150,000、Indirect Cost: ¥345,000)
Fiscal Year 2010: ¥1,625,000 (Direct Cost: ¥1,250,000、Indirect Cost: ¥375,000)
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| Keywords | 結び目 / ゴルディアン複体 / 幾何学 / トポロジー |
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| Research Abstract |
Ichihara and myself introduced new simplicial complexes by using various invariants and local moves for knots, which give generalizations of the Gordian complex. We focused on the simplicial complex defined by using the Alexander-Conway polynomial and the Delta-move, and showed that the simplicial complex is Gromov hyperbolic and quasi-isometric to the real line.
I studied the characterization problem on the Alexander polynomial of an alternating knot. In particular, I constructed infinitely many Alexander polynomials which satisfy a necessary condition to become the Alexander polynomials of alternating knots but which cannot be realized by an alternating knot.
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Report
(3 results)
Research Products
(26 results)
