The non-abelian topological torsion and the Iwasawa polynomial

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540068
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Chiba University
• Principal Investigator: SUGIYAMA Ken-ichi 千葉大学, 理学(系)研究科(研究院), 教授 (90206441)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 結び目群 / 双曲結び目 / ３次元双曲多様体

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.

Free Research Field

幾何学