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

Takahiro Kitayama

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arXiv · 0801.3819

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

Takahiro Kitayama

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Abstract

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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Takahiro Kitayama. 2009-09-17. Symmetry of Reidemeister torsion on $SU_2$-representation spaces of knots. https://arxiv.org/abs/0801.3819

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