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BIRS Workshop Lecture Videos

The mapping class group of minimal subshifts Yang, Kitty


Let $(X, \sigma)$ be a subshift and $\textrm{Aut}(X)$ be the automorphism group, the group of self conjugacies of $(X, \sigma)$. The mapping class group, denoted $\mathcal{M})(\sigma)$, is the group of self flow equivalences. We show that $\mathcal{M}(\sigma)$ is constrained in the case of low-complexity minimal subshifts, similar to constraints on $\textrm{Aut}(X)$. In particular, when $(X, \sigma)$ is a minimal subshift associated to a substitution, $\mathcal{M}(\sigma)$ is an extension of $\mathbb{Z}$ by some finite subgroup of $\textrm{Aut}(X)$.

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