A study on a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots
| Project/Area Number |
26400096
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Keio University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | DFJ予想 / 双曲結び目 / ねじれアレキサンダー多項式 / 結び目群 / ファイバー性 / 結び目種数 / 双曲的結び目 / パラボリック表現 |
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| Outline of Final Research Achievements |
The purpose of this research was to give an answer to a conjecture of Dunfiled, Friedl and Jackson on the genus and fiberedness of a hyperbolic knot. To this end, we used information on a certain slice of the character variety of the knot group and the twisted Alexander polynomial. The results are as follows.
(1) We showed that 2-bridge knots are classified by the defining polynomial of parabolic representations of the knot group.
(2) We gave an affirmative answer to a conjecture of Dunfiled, Friedl and Jackson for a hyperbolic pretzel knot with length three.
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Report
(5 results)
Research Products
(16 results)
