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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 S3 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