{"paper":{"title":"Acylindrical hyperbolicity and Artin-Tits groups of spherical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bert Wiest, Matthieu Calvez","submitted_at":"2016-06-24T18:11:24Z","abstract_excerpt":"We prove that, for any irreducible Artin-Tits group of spherical type $G$, the quotient of $G$ by its center is acylindrically hyperbolic. This is achieved by studying the additional length graph associated to the classical Garside structure on $G$, and constructing a specific element $x_G$ of $G/Z(G)$ whose action on the graph is loxodromic and WPD in the sense of Bestvina-Fujiwara; following Osin, this implies acylindrical hyperbolicity. Finally, we prove that \"generic\" elements of $G$ act loxodromically, where the word \"generic\" can be understood in either of the two common usages: as a res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07778","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"}