{"paper":{"title":"Vastness properties of automorphism groups of RAAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrew Sale, Vincent Guirardel","submitted_at":"2016-09-15T20:40:32Z","abstract_excerpt":"Outer automorphism groups of RAAGs, denoted $Out(A_\\Gamma)$, interpolate between $Out(F_n)$ and $GL_n(\\mathbb{Z})$. We consider several vastness properties for which $Out(F_n)$ behaves very differently from $GL_n(\\mathbb{Z})$: virtually mapping onto all finite groups, SQ-universality, virtually having an infinite dimensional space of homogeneous quasimorphisms, and not being boundedly generated.\n  We give a neccessary and sufficient condition in terms of the defining graph $\\Gamma$ for each of these properties to hold. Notably, the condition for all four properties is the same, meaning $Out(A_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04854","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"}