Knot invariants from

symbolic dynamical systems

Authors:
Daniel S. Silver and Susan G. Williams

Journal:
Trans. Amer. Math. Soc. **351** (1999), 3243-3265

MSC (1991):
Primary 57Q45; Secondary 54H20, 20E06, 20F05

DOI:
https://doi.org/10.1090/S0002-9947-99-02167-4

Published electronically:
April 7, 1999

MathSciNet review:
1466957

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If is the group of an oriented knot , then the set of representations of the commutator subgroup into any finite group has the structure of a shift of finite type , a special type of dynamical system completely described by a finite directed graph. Invariants of , such as its topological entropy or the number of its periodic points of a given period, determine invariants of the knot. When is abelian, gives information about the infinite cyclic cover and the various branched cyclic covers of . Similar techniques are applied to oriented links.

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Additional Information

**Daniel S. Silver**

Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688

Email:
silver@mathstat.usouthal.edu

**Susan G. Williams**

Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688

Email:
williams@mathstat.usouthal.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02167-4

Received by editor(s):
June 27, 1996

Received by editor(s) in revised form:
July 16, 1997

Published electronically:
April 7, 1999

Article copyright:
© Copyright 1999
American Mathematical Society