{"paper":{"title":"Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Catherine Pfaff, Yael Algom-Kfir","submitted_at":"2016-03-23T14:41:53Z","abstract_excerpt":"We let $\\varphi$ be an ageometric fully irreducible outer automorphism so that its Handel-Mosher axis bundle consists of a single unique axis. We show that the centralizer $Cen(\\langle\\varphi\\rangle)$ of the cyclic subgroup generated by $\\varphi$ equals the stabilizer $\\text{Stab}(\\Lambda^+_\\varphi)$ of the attracting lamination $\\Lambda^+_{\\varphi}$ and is isomorphic to $\\mathbb Z$. We further show, via an analogous result about the commensurator, that the normalizer $N(\\langle\\varphi\\rangle)$ of $\\langle \\varphi \\rangle$ is isomorphic to either $\\mathbb Z$ or $\\mathbb Z_2 * \\mathbb Z_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07206","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"}