{"paper":{"title":"Similar relatively hyperbolic actions of a group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Leonid Potyagailo, Victor Gerasimov","submitted_at":"2013-05-28T22:40:23Z","abstract_excerpt":"Let a discrete group $G$ possess two convergence actions by homeomorphisms on compacta $X$ and $Y$. Consider the following question: does there exist a convergence action $G{\\curvearrowright}Z$ on a compactum $Z$ and continuous equivariant maps $X\\leftarrow Z\\to Y$? We call the space $Z$ (and action of $G$ on it) {\\it pullback} space (action). In such general setting a negative answer follows from a recent result of O. Baker and T. Riley [BR].\n  Suppose, in addition, that the initial actions are relatively hyperbolic that is they are non-parabolic and the induced action on the distinct pairs a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6649","kind":"arxiv","version":3},"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"}