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

Published in Annales de l'Institut Fourier. 2005, vol. 55, no. 5, p. 1685-1734
Abstract For a knot K in $S^3$ and a regular representation $ ho$ 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.
Stable URL https://archive-ouverte.unige.ch/unige:12203
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Deposited on : 2010-10-21

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