Dynamics of Twisted Alexander Invariants

dc.creatorSilver, Daniel S.
dc.creatorWilliams, Susan G.
dc.date2008-01-14
dc.date2009-04-30
dc.date.accessioned2026-07-07T13:09:39Z
dc.date.available2026-07-07T13:09:39Z
dc.descriptionThe 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.descriptionThis version contains corrections and improvements in exposition. 38 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0801.2118
dc.identifierhttp://arxiv.org/abs/0801.2118
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228806
dc.subjectGeometric Topology
dc.subjectDynamical Systems
dc.subject57M25; 37B40
dc.titleDynamics of Twisted Alexander Invariants
dc.typetext

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