{"paper":{"title":"Vertex finiteness for splittings of relatively hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Gilbert Levitt, Vincent Guirardel","submitted_at":"2013-11-12T16:50:26Z","abstract_excerpt":"Consider a group G and a family $\\mathcal{A}$ of subgroups of G. We say that vertex finiteness holds for splittings of G over $\\mathcal{A}$ if, up to isomorphism, there are only finitely many possibilities for vertex stabilizers of minimal G-trees with edge stabilizers in $\\mathcal{A}$.\n  We show vertex finiteness when G is a toral relatively hyperbolic group and $\\mathcal{A}$ is the family of abelian subgroups.\n  We also show vertex finiteness when G is hyperbolic relative to virtually polycyclic subgroups and $\\mathcal{A}$ is the family of virtually cyclic subgroups; if moreover G is one-end"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2835","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"}