{"paper":{"title":"The Mapping Class Group of a Minimal Subshift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kitty Yang, Scott Schmieding","submitted_at":"2018-10-20T19:51:14Z","abstract_excerpt":"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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08847","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}