{"paper":{"title":"Cell-Like Equivalences and Boundaries of CAT(0) Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christopher Mooney, Craig Guilbault","submitted_at":"2010-11-05T00:10:11Z","abstract_excerpt":"In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than one boundary. This contrasted with the situation for word hyperbolic groups, where it was well-known that each such group admitted a unique boundary---in a very stong sense. Prior to Croke and Kleiner's discovery, it had been observed by Geoghegan and Bestvina that a weaker sort of uniquness does hold for boundaries of torsion free CAT(0) groups; in particular, any two such boundaries always have the same shape. Hence, the boundary really does carry significant information about the group itself. In an attempt to stren"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1298","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"}