{"paper":{"title":"Dilatation of outer automorphisms of Right-angled Artin Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Corey Bregman, Yulan Qing","submitted_at":"2018-10-15T16:25:07Z","abstract_excerpt":"We study the dilatation of outer automorphisms of right-angled Artin groups. Given a right-angled Artin group defined on a simplicial graph: $A(\\Gamma) = \\langle V | E \\rangle$ and an automorphism $\\phi \\in Out(A(\\Gamma))$ there is a natural measure of how fast the length of a word of $A(\\Gamma)$ grows after $n$ iterations of $\\phi$ as a function of $n$, which we call the dilatation of $w$ under $\\phi$. We define the dilatation of $\\phi$ as the supremum over dilatations of all $w \\in A(\\Gamma)$. Assuming that $\\phi$ is a pure and square map, we show that if the dilatation of $\\phi$ is positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06499","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"}