{"paper":{"title":"Fundamental group of uniquely ergodic Cantor minimal systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Norio Nawata","submitted_at":"2011-07-13T09:10:34Z","abstract_excerpt":"We introduce the fundamental group ${\\mathcal F}(\\mathcal{R}_{G, \\phi})$ of a uniquely ergodic Cantor minimal $G$-system $\\mathcal{R}_{G, \\phi}$ where $G$ is a countable discrete group. We compute fundamental groups of several uniquely ergodic Cantor minimal $G$-systems. We show that if $\\mathcal{R}_{G, \\phi}$ arises from a free action $\\phi$ of a finitely generated abelian group, then there exists a unital countable subring $R$ of $\\mathbb{R}$ such that $\\mathcal{F}(\\mathcal{R}_{G, \\phi})=R_{+}^\\times$. We also consider the relation between fundamental groups of uniquely ergodic Cantor minima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2493","kind":"arxiv","version":2},"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"}