Dynamics of Twisted Alexander Invariants
| dc.creator | Silver, Daniel S. | |
| dc.creator | Williams, Susan G. | |
| dc.date | 2008-01-14 | |
| dc.date | 2009-04-30 | |
| dc.date.accessioned | 2026-07-07T13:09:39Z | |
| dc.date.available | 2026-07-07T13:09:39Z | |
| dc.description | 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. | |
| dc.description | This version contains corrections and improvements in exposition. 38 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0801.2118 | |
| dc.identifier | http://arxiv.org/abs/0801.2118 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228806 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | 57M25; 37B40 | |
| dc.title | Dynamics of Twisted Alexander Invariants | |
| dc.type | text |