{"paper":{"title":"Finite generating sets of relatively hyperbolic groups and applications to geodesic languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Laura Ciobanu, Yago Antol\\'in","submitted_at":"2014-02-12T21:12:18Z","abstract_excerpt":"Given a finitely generated relatively hyperbolic group $G$, we construct a finite generating set $X$ of $G$ such that $(G,X)$ has the `falsification by fellow traveler property' provided that the parabolic subgroups $\\{H_\\omega\\}_{\\omega\\in \\Omega}$ have this property with respect to the generating sets $\\{X\\cap H_\\omega\\}_{\\omega\\in \\Omega}$. This implies that groups hyperbolic relative to virtually abelian subgroups, which include all limit groups and groups acting freely on $\\mathbb{R}^n$-trees, or geometrically finite hyperbolic groups, have generating sets for which the language of geodes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2985","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"}