The mapping class group of a minimal subshift

Scott Schmieding, Kitty Yang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


For a homeomorphism T: X → X of a Cantor set X, the mapping class group M(T ) is the group of isotopy classes of orientation-preserving self-homeomorphisms of the suspension ΣT X. The group M(T ) can be interpreted as the symmetry group of the system (X, T ) with respect to the flow equivalence relation. We study M(T ), focusing on the case when (X, T ) is a minimal subshift. We show that when (X, T ) is a subshift associated to a substitution, the group M(T ) is an extension of Z by a finite group; for a large class of substitutions including Pisot type, this finite group is a quotient of the automorphism group of (X, T ). When (X, T ) is a minimal subshift of linear complexity satisfying a no-infinitesimals condition, we show that M(T ) is virtually abelian. We also show that when (X, T ) is minimal, M(T ) embeds into the Picard group of the crossed product algebra C(X) ⋊T Z.

Original languageEnglish (US)
Pages (from-to)233-265
Number of pages33
JournalColloquium Mathematicum
Issue number2
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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