{"paper":{"title":"Assembling homology classes in automorphism groups of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.QA"],"primary_cat":"math.AT","authors_text":"Allen Hatcher, James Conant, Karen Vogtmann, Martin Kassabov","submitted_at":"2015-01-10T13:03:04Z","abstract_excerpt":"The observation that a graph of rank $n$ can be assembled from graphs of smaller rank $k$ with $s$ leaves by pairing the leaves together leads to a process for assembling homology classes for $Out(F_n)$ and $Aut(F_n)$ from classes for groups $\\Gamma_{k,s}$, where the $\\Gamma_{k,s}$ generalize $Out(F_k)=\\Gamma_{k,0}$ and $Aut(F_k)=\\Gamma_{k,1}$. The symmetric group $\\Sigma_s$ acts on $H_*(\\Gamma_{k,s})$ by permuting leaves, and for trivial rational coefficients we compute the $\\Sigma_s$-module structure on $H_*(\\Gamma_{k,s})$ completely for $k \\leq 2$. Assembling these classes then produces all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02351","kind":"arxiv","version":4},"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"}