Cobordism categories of manifolds with Baas-Sullivan singularities, Part 2

Abstract

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 manifolds with corners from arXiv:0810.0581.

39 pages, simplified many of the definitions, notational conventions, and proofs

References in corpus (2)

• A short exposition of the Madsen-Weiss theorem
• Introduction to the manifold calculus of Goodwillie-Weiss

Cited by in corpus (3)

• Stable Moduli Spaces of High Dimensional Handlebodies
• Homological Stability for Diffeomorphism Groups of High Dimensional Handlebodies
• Stability for moduli spaces of manifolds with conical singularities