{"paper":{"title":"Ends of Schreier graphs and cut-points of limit spaces of self-similar groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Daniele D'Angeli, Ievgen Bondarenko, Tatiana Nagnibeda","submitted_at":"2016-01-27T22:17:58Z","abstract_excerpt":"Every self-similar group acts on the space $X^\\omega$ of infinite words over some alphabet $X$. We study the Schreier graphs $\\Gamma_w$ for $w\\in X^\\omega$ of the action of self-similar groups generated by bounded automata on the space $X^\\omega$. Using sofic subshifts we determine the number of ends for every Schreier graph $\\Gamma_w$. Almost all Schreier graphs $\\Gamma_w$ with respect to the uniform measure on $X^\\omega$ have one or two ends, and we characterize bounded automata whose Schreier graphs have two ends almost surely. The connection with (local) cut-points of limit spaces of self-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07587","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"}