{"paper":{"title":"Boundary classification and 2-ended splittings of groups with isolated flats","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Matthew Haulmark","submitted_at":"2017-04-26T00:04:57Z","abstract_excerpt":"In this paper we provide a classification theorem for 1-dimensional boundaries of groups with isolated flats. Given a group $\\Gamma$ acting geometrically on a $CAT(0)$ space $X$ with isolated flats and 1-dimensional boundary, we show that if $\\Gamma$ does not split over a virtually cyclic subgroup, then $\\partial X$ is homeomorphic to a circle, a Sierpinski carpet, or a Menger curve. This theorem generalizes a theorem of Kapovich-Kleiner, and resolves a question due to Kim Ruane.\n  We also study the relationship between local cut points in $\\partial X$ and splittings of $\\Gamma$ over $2$-ended"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07937","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"}