{"paper":{"title":"Relations between various boundaries of relatively hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.GR","authors_text":"Hung Cong Tran","submitted_at":"2012-12-12T02:05:26Z","abstract_excerpt":"Suppose a group $G$ is relatively hyperbolic with respect to a collection $\\PP$ of its subgroups and also acts properly, cocompactly on a $\\CAT(0)$ (or $\\delta$--hyperbolic) space $X$. The relatively hyperbolic structure provides a relative boundary $\\partial(G,\\PP)$. The $\\CAT(0)$ structure provides a different boundary at infinity $\\partial X$. In this article, we examine the connection between these two spaces at infinity. In particular, we show that $\\partial (G,\\PP)$ is $G$--equivariantly homeomorphic to the space obtained from $\\partial X$ by identifying the peripheral limit points of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2688","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"}