The Mapping Class Group of a Shift of Finite Type

Abstract

We study the mapping class group of a nontrivial irreducible shift of finite type: the group of flow equivalences of its mapping torus modulo isotopy. This group plays for flow equivalence the role that the automorphism group plays for conjugacy. It is countable; not residually finite; acts faithfully (and n-transitively, for all n) by permutations on the set of circles in the mapping torus; has solvable word problem and trivial center; etc. There are many open problems.

28 pages. Theorem 3.6 of version 1 is withdrawn and replaced by Remark 3.6. Other changes are minor corrections and expanded/improved exposition