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- W2896819452 abstract "For a homeomorphism $T colon X to X$ of a Cantor set $X$, the mapping class group $mathcal{M}(T)$ is the group of isotopy classes of orientation-preserving self-homeomorphisms of the suspension $Sigma_{T}X$. The group $mathcal{M}(T)$ can be interpreted as the symmetry group of the system $(X,T)$ with respect to the flow equivalence relation. We study $mathcal{M}(T)$, 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 $mathcal{M}(T)$ is an extension of $mathbb{Z}$ 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 $mathcal{M}(T)$ is virtually abelian. We also show that when $(X,T)$ is minimal, $mathcal{M}(T)$ embeds into the Picard group of the crossed product algebra $C(X) rtimes_{T} mathbb{Z}$." @default.
- W2896819452 created "2018-10-26" @default.
- W2896819452 creator A5073064277 @default.
- W2896819452 creator A5076813405 @default.
- W2896819452 date "2018-10-20" @default.
- W2896819452 modified "2023-10-16" @default.
- W2896819452 title "The Mapping Class Group of a Minimal Subshift" @default.
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- W2896819452 doi "https://doi.org/10.48550/arxiv.1810.08847" @default.
- W2896819452 hasPublicationYear "2018" @default.
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