Studies on partial orders on sets of 3-manifolds defined by epimorphisms between fundamental groups.
| Project/Area Number |
21540100
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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 | Soka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MORIFUJI Takayuki 慶應義塾大学, 経済学部, 教授 (90334466)
SUZUKI Masaaki 秋田大学, 教育文化学部, 准教授 (70431616)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 3次元多様体 / 結び目 / 基本群 / 有限素体 / 結び目群 / 非可換表現 / 全射準同型写像 / metabelian表現 / 写像度 / Casson不変量 / ねじれAlexander不変量 / 半順序関係 / degree |
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| Research Abstract |
For the set of prime knots with up to 11-crossings, we determined the partial order relation defined by using meridian preserving epimorphisms between knots groups. We also proved that for any given 2-bridge knot there exists a Montesinos knot with an epimorphims which is induced by a degree zero map. Further we found pairs of a 3-bridge hyperbolic Montsinos knot and a 2-bridge hyperbolic knot which is not induced from a nonzero degree map. For any knot, there exists a infinitely many prime numbers such that there exists a non abelian representation on its knot group in 2-dimensional special linear group over a finite prime field with such a characteristic.
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Report
(4 results)
Research Products
(24 results)
