The mapping class group of a shift of finite type
Copyright policy )The mapping class group of a shift of finite type
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 Theorem 3.6 of version 1 is withdrawn and replaced by Remark 3.6.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
shift of finite type, Symbolic dynamics, automorphism group, Multi-dimensional shifts of finite type, tiling dynamics, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), mapping class group, Dynamical Systems (math.DS), FOS: Mathematics, 37B10 (Primary), 20F10, 20F38 (Secondary), flow equivalence, Mathematics - Dynamical Systems, Other groups related to topology or analysis
shift of finite type, Symbolic dynamics, automorphism group, Multi-dimensional shifts of finite type, tiling dynamics, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), mapping class group, Dynamical Systems (math.DS), FOS: Mathematics, 37B10 (Primary), 20F10, 20F38 (Secondary), flow equivalence, Mathematics - Dynamical Systems, Other groups related to topology or analysis
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