{"paper":{"title":"Topological freeness for $*$-commuting covering maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Nicolai Stammeier","submitted_at":"2013-11-04T17:51:10Z","abstract_excerpt":"A countable family of $*$-commuting surjective, non-injective local homeomorphisms of a compact Hausdorff space $X$ gives rise to an action $\\theta$ of a countably generated, free abelian monoid $P$. For such a triple $(X,P,\\theta)$, which we call an irreversible $*$-commutative dynamical system, we construct a universal $C^*$-algebra $\\mathcal{O}[X,P,\\theta]$. Within this setting we show that the following four conditions are equivalent: $(X,P,\\theta)$ is topologically free, $C(X) \\subset \\mathcal{O}[X,P,\\theta]$ has the ideal intersection property, the natural representation of $\\mathcal{O}["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0793","kind":"arxiv","version":3},"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"}