Symmetry of Reidemeister torsion on $S{U}_2$-representation spaces of knots

Abstract

We study two sorts of actions on the space of conjugacy classes of irreducible $S{U}_2$-representations of a knot group. One of them is an involution which comes from the algebraic structure of $S{U}_2$ and the other is the action by the outer automorphism group of the knot group. In particular, we consider them on an 1-dimensional smooth part of the space, which is canonically oriented and metrized via a Reidemeister torsion volume form. As an application we show that the Reidemeister torsion function on the 1-dimensional subspace has symmetry about the metrization.

18 pages, 2 figures; 11 pages, 2 figures, rewritten in terms of Reidemeister torsion instead of twisted Alexander invariants; 12 pages, 2 figures, to appear in Topology and its Applications