Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups

2004/03/26 by Jérôme Dubois, Dubois, Jérôme
Mathematics · #57M25 #57M27 #57Q10 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:57M25 #msc:57M27 #msc:57Q10

paper · pdf · doi:10.48550/arxiv.math/0403470

36 pages, 2 figures. to appear in Ann. Institut Fourier

openalex publication_date 2004/03/26 · arxiv created 2005/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a knot K in S³ and a regular representation ρ of its group G_K into SU(2) we construct a non abelian Reidemeister torsion on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion provides a volume form on the SU(2)-representation space of G_K. In another way, we construct according to Casson--or more precisely taking into account Lin's and Heusener's further works--a volume form on the SU(2)-representation space of G_K. Next, we compare these two apparently different points of view--the first by means of the Reidemeister torsion and the second defined ``a la Casson"--and finally prove that they define the same topological knot invariant.

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