{"paper":{"title":"Cobordism categories of manifolds with Baas-Sullivan singularities, Part 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AT","authors_text":"Nathan Perlmutter","submitted_at":"2013-06-18T00:08:45Z","abstract_excerpt":"For a given list of closed manifolds $\\Sigma_k=(P_1,...,P_k)$, we construct a cobordism category $\\mathbf{Cob}_{d}^{\\Sigma_{k}}$ of embedded manifolds with Baas-Sullivan singularities of type $\\Sigma_k$. Our main results identify the homotopy type of the classifying spaces $B\\mathbf{Cob}_{d}^{\\Sigma_{k}}$ of these cobordism categories with that of the infinite loop-space of a certain spectrum, $\\mathsf{MT}_{\\Sigma_{k}}(d)$. Our results generalize of the work of Galatius, Madsen, Tillmann, and Weiss from arXiv:math/0605249. It also generalizes the work of Genauer on the cobordism categories of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4045","kind":"arxiv","version":3},"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"}