{"paper":{"title":"Normal form and parabolic dynamics for quadratically growing automorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kaidi Ye, Martin Lustig","submitted_at":"2017-05-11T11:06:52Z","abstract_excerpt":"We present a normal form for outer automorphisms $\\phi$ of a non-abelian free group $F_N$ which grow quadratically (measured through the maximal growth of conjugacy classes in $F_N$ under iteration of $\\phi$). In analogy to the known normal form for linearly growing automorphisms as efficient Dehn twist, our normal form for $\\phi$ is given in terms of a 2-level Dehn twist on a graph-of-groups $\\cal{G}$ with $\\pi_1 {\\cal{G}} \\cong F_N$, where a conjugacy class of $F_N$ grows at most linearly if and only if it is contained in a vertex group of $\\cal{G}$.\n  Our proof is based on earlier work of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04110","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"}