Dynamics of Twisted Alexander Invariants

Details Dynamics of Twisted Alexander Invariants Dynamics of Twisted Alexander Invariants

2008-01-14

arxiv.org/abs/0801.2118v3

Mathematics

Geometric Topology

This version contains corrections and improvements in exposition. 38 pages, 4 figures

Scientific paper

The Pontryagin dual of the twisted Alexander module for a d-component link and GL(N,Z) representation is an algebraic dynamical system with an elementary description in terms of colorings of a diagram. In the case of a knot, its associated topological entropy is the logarithmic growth rate of the number of torsion elements in the twisted first-homology group of r-fold cyclic covers of the knot complement, as r goes to infinity. Total twisted representations are introduced, and their properties are studied. The twisted Alexander polynomial obtained from any nonabelian parabolic SL(2,C) representation of a 2-bridge knot group is seen to be nontrivial. The zeros of any twisted Alexander polynomial of a torus knot corresponding to a parabolic SL(2,C) representation or a finite-image permutation representation are shown to be roots of unity.

Affiliated with

Also associated with

No associations

Rating

Dynamics of Twisted Alexander Invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamics of Twisted Alexander Invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics of Twisted Alexander Invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-634665