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Organizers |
Knot group symmetries and Markov subgroups
by
Daniel S. Silver
University of South Alabama
Coauthors: Susan G. Williams
Let G be the group of an oriented knot k subset S3 and let \chi:G --> Z be the homomorphism that maps each meridianal generator to 1. Let K be the kernel of \chi, the commutator subgroup of G. For any finite group \Sigma, the set Hom(K, \Sigma) has the structure of a shift of finite type \Phi\Sigma, a symbolic dynamical system with attractive properties. General properties of \Phi\Sigma have been studied by the authors. When \Sigma is abelian, \Phi\Sigma has the additional structure of an abelian group. It is an example of a Markov subgroup. Its structure contains obstructions to periodicity for the knot k. Many of our techniques apply to oriented knots and links in any dimension.
Date received: February 12, 1998
Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caas-62.