{"paper":{"title":"Every Infinite order mapping class has an infinite order action on the homology of some finite cover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Asaf Hadari","submitted_at":"2015-08-06T22:28:32Z","abstract_excerpt":"We prove the following well known conjecture: let $\\Sigma$ be an oriented surface of finite type whose fundamental group is a nonabelian free group. Let $\\phi \\in \\textup{Mod}(\\Sigma)$ be a an infinite order mapping class. Then there exists a finite solvable cover $\\widehat{\\Sigma} \\to \\Sigma$, and a lift $\\widehat{\\phi}$ of $\\phi$ such that the action of $\\widehat{\\phi}$ on $H_1(\\widehat{\\Sigma}, \\mathbb{Z})$ has infinite order. Our main tools are the theory of homological shadows, which was previously developed by the author, and Fourier analysis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01555","kind":"arxiv","version":1},"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"}