Pro-finite completion of a 3-manifold group and its relation to topological invariants
| Project/Area Number |
25400101
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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 | Soka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MORIFUJI Takayuki 慶応義塾大学, 経済学部, 教授 (90334466)
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| Research Collaborator |
TRAN Anh University of Texas at Dallas
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 基本群 / Reidemeister torsion / linear representation / fundamental group / SL(2;C)-representation / minimal polynomial / Brieskorm manifold / homology sphere / homology 3-sphere / torus knot / figure-eight knot / Reidemeister torison / Dehn surgery / Brieskorn manifold / Chebychev polynomial / 結び目 / トーラス結び目 / 副有限完備化 / 自由積 |
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| Outline of Final Research Achievements |
We studied 3-dimensional topology from the view point of the pro-finite completion of the fundamental group of a 3-manifold manifold. In particular we studied Reiemeister torsion for SL(2;C)-representations, which is defined by using linear representations of the fundamental group.Denis Johnson proposed some theory related with Reidemeister torsion. We obtained some formula of Reidemeister torsion, which would be related with Galois group, or Galois extensions of a field.
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Report
(5 results)
Research Products
(14 results)
