{"paper":{"title":"Comparison radius and mean topological dimension: $\\mathbb{Z}^d$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Zhuang Niu","submitted_at":"2019-06-21T14:47:58Z","abstract_excerpt":"Consider a minimal free topological dynamical system $(X, T, \\mathbb{Z}^d)$. It is shown that the comparison radius of the crossed product C*-algebra $\\mathrm{C}(X) \\rtimes \\mathbb{Z}^d$ is at most the half of the mean topological dimension of $(X, T, \\mathbb{Z}^d)$. As a consequence, the C*-algebra $\\mathrm{C}(X) \\rtimes \\mathbb{Z}^d$ is classifiable if $(X, T, \\mathbb{Z}^d)$ has zero mean dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09171","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"}