{"paper":{"title":"Stable Moduli Spaces of High Dimensional Handlebodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Boris Botvinnik, Nathan Perlmutter","submitted_at":"2015-09-10T23:14:44Z","abstract_excerpt":"We study the moduli space of handlebodies diffeomorphic to $(D^{n+1}\\times S^{n})^{\\natural g}$, i.e. the classifying space $BDiff((D^{n+1}\\times S^n)^{\\natural g}, D^{2n})$ of the group of diffeomorphisms that restrict to the identity near a $2n$-dimensional disk embedded in the boundary, $\\partial(D^{n+1}\\times S^n)^{\\natural g}$. We construct a map $colim_{g\\to\\infty}BDiff((D^{n+1}\\times S^n)^{\\natural g}, D^{2n}) \\longrightarrow Q_{0}BO(2n+1)\\langle n \\rangle_{+}$ and prove that it induces an isomorphism on integral homology in the case that $2n+1 \\geq 9$. Above, $BO(2n+1)\\langle n \\rangle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03359","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"}