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

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.