#### Volume 6, issue 1 (2006)

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A volume form on the $\mathrm{SU}(2)$–representation space of knot groups

### Jérôme Dubois

Algebraic & Geometric Topology 6 (2006) 373–404
 arXiv: math.GT/0409529
##### Abstract

For a knot $K$ in ${S}^{3}$ we construct according to Casson—or more precisely taking into account Lin and Heusener’s further works—a volume form on the $SU\left(2\right)$–representation space of the group of $K$. We prove that this volume form is a topological knot invariant and explore some of its properties.

##### Keywords
knot groups, representation space, volume form, Casson invariant, adjoint representation, SU
##### Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M05, 57M27
##### Publication
Received: 24 September 2004
Revised: 25 August 2005
Accepted: 27 December 2005
Published: 12 March 2006
##### Authors
 Jérôme Dubois Section de Mathématiques Université de Genève CP 64 2–4 Rue du Lièvre CH-1211 Genève 4 Switzerland