NON-ABELIAN REIDEMEISTER TORSION FOR TWIST KNOTS

Abstract

This paper gives an explicit formula for the SL 2 (ℂ)-non-abelian Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the non-abelian Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot.