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Jérôme Dubois
Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups
(Torsion de Reidemeister non abélienne et forme volume sur l'espace des représentations du groupe d'un noeud dans SU(2))
Annales de l'institut Fourier, 55 no. 5 (2005), p. 1685-1734, doi: 10.5802/aif.2136
Article PDF | Reviews MR 2172277 | Zbl 1077.57009 | 1 citation in Cedram
Class. Math.: 57M25, 57Q10, 57M27
Keywords: Knot groups, representation space, volume form, Reidemeister torsion, Casson invariant, adjoint representation, SU(2)

Résumé - Abstract

For a knot $K$ in the 3-sphere and a regular representation of its group $G_K$ into SU(2) we construct a non abelian Reidemeister torsion form on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion form provides a volume form on the SU(2)-representation space of $G_K$. In another way, we construct using Casson's original construction a natural volume form on the SU(2)-representation space of $G_K$. Next, we compare these two apparently different points of view on the representation variety and finally prove that they produce the same topological knot.

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