Israel Journal of Mathematics

, Volume 95, Issue 1, pp 231–251

Augmented group systems and shifts of finite type

Authors

    • Department of Mathematics and StatisticsUniversity of South Alabama
  • Susan G. Williams
    • Department of Mathematics and StatisticsUniversity of South Alabama
Article

DOI: 10.1007/BF02761041

Cite this article as:
Silver, D.S. & Williams, S.G. Israel J. Math. (1996) 95: 231. doi:10.1007/BF02761041

Abstract

Let (G, χ, x) be a triple consisting of a finitely presented groupG, epimorphism χ:GZ, and distinguished elementxG such that χ(x)=1. Given a finite symmetric groupSr, we construct a finite directed graph Γ that describes the set Φr of representations π: Ker χ →Sr as well as the mapping σxr→Φr defined by (σxϱ)(a) = ϱ(x−1ax) for alla ∈ Ker χ. The pair (Φrx has the structure of a shift of finite type, a well-known type of compact 0-dimensional dynamical system. We discuss basic properties and applications of therepresentation shiftrx), including applications to knot theory.

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© The Magnes Press 1996