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An invariant of finite group actions on shifts of finite type

Published online by Cambridge University Press:  15 September 2005

DANIEL S. SILVER  and
SUSAN G. WILLIAMS
DANIEL S. SILVER
Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA (e-mail: silver@jaguar1.usouthal.edu, swilliam@jaguar1.usouthal.edu)
SUSAN G. WILLIAMS
Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA (e-mail: silver@jaguar1.usouthal.edu, swilliam@jaguar1.usouthal.edu)
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Abstract

We describe a pair of invariants for actions of finite groups on shifts of finite type, the left-reduced and right-reduced shifts. The left-reduced shift was first constructed by Fiebig, who showed that its zeta function is an invariant, and in fact equal to the zeta function of the quotient dynamical system. We also give conditions for expansivity of the quotient, and applications to combinatorial group theory, knot theory and topological quantum field theory.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 6 , December 2005 , pp. 1985 - 1996
Copyright
2005 Cambridge University Press

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