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

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

2004-03-26

arxiv.org/abs/math/0403470v4

Mathematics

Geometric Topology

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

Scientific paper

For a knot K in $S^3$ and a regular representation $\rho$ 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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