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English

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

ContributorsDubois, Jérôme
Published inAnnales de l'Institut Fourier, vol. 55, no. 5, p. 1685-1734
Publication date2005
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.

Classification
  • arxiv : math.GT
Citation (ISO format)
DUBOIS, Jérôme. Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups. In: Annales de l’Institut Fourier, 2005, vol. 55, n° 5, p. 1685–1734. doi: 10.5802/aif.2136
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ISSN of the journal0373-0956
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