Symmetry of Reidemeister torsion on $SU_2$-representation spaces of knots

Details Symmetry of Reidemeister torsion on $SU_2$-representation spaces of knots Symmetry of Reidemeister torsion on $SU_2$-representation spaces of knots

2008-01-24

arxiv.org/abs/0801.3819v3

Topology Appl. 156 (2009) 2772-2781

Mathematics

Geometric Topology

18 pages, 2 figures; 11 pages, 2 figures, rewritten in terms of Reidemeister torsion instead of twisted Alexander invariants;

Scientific paper

We study two sorts of actions on the space of conjugacy classes of irreducible $SU_2$-representations of a knot group. One of them is an involution which comes from the algebraic structure of $SU_2$ 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.

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