{"paper":{"title":"Commensurability of groups quasi-isometric to RAAG's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Jingyin Huang","submitted_at":"2016-03-28T23:04:39Z","abstract_excerpt":"Let $G$ be a right-angled Artin group with defining graph $\\Gamma$ and let $H$ be a finitely generated group quasi-isometric to $G(\\Gamma)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $\\Gamma$ does not have induced 4-cycle; (3) $\\Gamma$ is star-rigid; then $H$ is commensurable to $G$. We show condition (2) is sharp in the sense that if $\\Gamma$ contains an induced 4-cycle, then there exists an $H$ quasi-isometric to $G(\\Gamma)$ but not commensurable to $G(\\Gamma)$. Moreover, one can drop condition (1) if $H$ is a uniform lattice acting on the universal cover of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08586","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"}