Symmetry of Reidemeister torsion on SU

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• 作者：Takahiro Kitayama
• 关键词：Knot ; Reidemeister torsion ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1K-4X3DRTK-2&_mathId=mml4&_user=10&_cdi=5677&_pii=S0166864109004003&_rdoc=10&_issn=01668641&_acct=C000029478&_v
• 刊名：Topology and its Applications
• 出版年：2009
• 出版时间：1 November 2009
• 年：2009
• 卷：156
• 期：17
• 页码：2772-2781
• 全文大小：229 K

文摘

We study two sorts of actions on the space of conjugacy classes of irreducible SU₂-representations of a knot group. One of them is an involution which comes from the algebraic structure of SU₂ and the other is the action by the outer automorphism group of the knot group. In particular, we consider them on a 1-dimensional smooth part of the space, which is canonically oriented and metrized via a Reidemeister torsion volume form. As an application we show that the Reidemeister torsion function on the 1-dimensional subspace has symmetry about the metrization.