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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.03359","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-09-10T23:14:44Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"8f2ac72020f4b1cb819f3dea60940865b8ab53f7539772e5cb64ba6c3266a6b4","abstract_canon_sha256":"ae8f851f1b601fe59b1a1c550c4a145b409f15fbee42d894cbcb5ebdb9d872c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:25.198010Z","signature_b64":"bd2EmTdcvzMjRFtm2mfBvgs+IhQVxAdx1Ez8TCNm+2HfLKwH4uPwwLLsgXNrgWjshoV87ZdkHdRfzunEPM9xDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec264e7f58eb86bee5b7d037b3e6bd57a2f52ebc360fd47568016ee75673db7","last_reissued_at":"2026-05-18T00:44:25.197456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:25.197456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $2n+1 \\geq 9$. 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