{"paper":{"title":"Homological Stability for Diffeomorphism Groups of High Dimensional Handlebodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Nathan Perlmutter","submitted_at":"2015-10-09T05:15:43Z","abstract_excerpt":"In this paper we prove a homological stability theorem for the diffeomorphism groups of high dimensional manifolds with boundary, with respect to forming the boundary connected sum with the product $D^{p+1}\\times S^{q}$ for $|q - p| < \\min\\{p, q\\} - 2$. In a recent joint paper with Boris Botvinnik (see arXiv:1509.03359 ), we identify the homology of $colim_{g\\to \\infty}BDiff((D^{n+1}\\times S^{n})^{\\natural g}, \\; D^{2n})$ with that of the infinite loopspace $Q_{0}BO(2n+1)\\langle n\\rangle_{+}$, in the case that $n \\geq 4$. Combining this \"stable homology\" calculation with this paper's homologic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02571","kind":"arxiv","version":5},"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"}