Étude d'une forme volume naturelle sur l'espace de représentations du groupe d'un nœud dans SU(2)

For a knot K in S³, we construct in the line of Casson – or more precisely taking into account Lin's (J. Differential Geom. 35 (1992) 337–357) and Heusener's (Topology Appl. 127 (2003) 175–197) further works – a 1-volume form on the SU(2)-representation space of the group of K and we show how to interpret this volume form as a Reidemeister torsion. In the last part of this Note, we give an explicit computation of this volume form for torus knots. To cite this article: J. Dubois, C. R. Acad. Sci. Paris, Ser. I 336 (2003).