Yoshikazu Yamaguchi

NON-ABELIAN REIDEMEISTER TORSION FOR TWIST KNOTS

This paper gives an explicit formula for the SL2(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.

Limit values of the non-acyclic Reidemeister torsion for knots

We consider the Reidemeister torsion associated with SL2.C/‐representations of a knot group. A bifurcation point in the SL2.C/‐character variety of a knot group is a character which is given by both an abelian SL2.C/‐representation and a nonabelian one. We show that there exist limits of the non-acyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper. 57Q10; 57M05

The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary

We provide the twisted Alexander polynomials of finite abelian covers over three-dimensional manifolds whose boundary is a finite union of tori. This is a generalization of a well-known formula for the usual Alexander polynomial of knots in finite cyclic branched covers over the three-dimensional sphere.

The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots

We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL(2;C)-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We also give the set of the limits of the leading coefficients in the higher dimensional Reidemeister torsion explicitly.