The non-abelian topological torsion and the Iwasawa polynomial
| Project/Area Number |
22540068
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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 | Chiba University |
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Principal Investigator |
SUGIYAMA Ken-ichi 千葉大学, 理学(系)研究科(研究院), 教授 (90206441)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 結び目群 / 双曲結び目 / ３次元双曲多様体 / A多項式 / 結び目 / 不変量 / Weil予想 / 虚数乗法 / 基本群 / 超幾何方程式 / 特性曲線 / Jones汎関数 / 楕円曲線 / L関数 / 特殊値 / 岩澤理論 / Birch & Swinnerton-Dyer予想 / Tate予想 / 測度 / オイラー系 / 岩澤多項式 / 非可換類体論 / 写像類群 / 多重対数関数 / Magnus展開 |
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| Outline of Final Research Achievements |
The geometric structure of the complement of a knot in the three dimensional sphere is determined by its fundamental group. The group is called the knot group. If the complement admits a complete hyperbolic structure of finite volume the knot group is nothing but the Kleinian group which is a discrete subgroup of the 2×2 special linear group. It is an important object both in geometry and in number theory. Our research is to investigate how the knot group changes if one alters a crossing of a knot. If moreover the complement admits a complete hyperbolic metric of finite volume we have also studied the change of the hyperbolic structure. We also study a similarity between the Alexander polynomial and the Hasse-Weil congruent zeta function.
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Report
(6 results)
Research Products
(4 results)
