A volume form on the SU(2)–representation space of knot groups

Dubois, Jérôme

doi:10.2140/agt.2006.6.373

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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

DOI: 10.2140/agt.2006.6.373

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 $SU (2)$ –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

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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

Volume 6, issue 1 (2006)