Limit values of the non-acyclic Reidemeister torsion for knots

Details Limit values of the non-acyclic Reidemeister torsion for knots Limit values of the non-acyclic Reidemeister torsion for knots

2005-12-13

arxiv.org/abs/math/0512277v5

Mathematics

Geometric Topology

to appear in Algebraic and Geometric Topology

Scientific paper

We consider the Reidemeister torsion associated with SL(2, C)-representations of a knot group. A bifurcation point in the SL(2, C)-character variety of a knot group is a character which is given by both an abelian SL(2, C)-representation and a non-abelian 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.

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