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In a recent paper, we showed that groups admitting "veelike actions" on afinite language embed in mapping class groups of certain two-sided subshifts.In this note, we illustrate this theorem for the embedding of Thompson's $V$ byexhibiting the piecewise linear local rules for the embedding. These turn outto split the embedding into the mapping class group, showing that $V$ evenembeds in the mapping class group by homeomorphisms.

Thompson's $V$ in MCG of mixing SFT by PW-linear homeos