Soren Galatius, Ib Madsen, Ulrike Tillmann, Michael Weiss
Published 2006-05-10, updated 2010-09-21Version 3
The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d=2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one.
Comments: 40 pages. v2 has improved notation, added explanations, and minor mistakes fixed. v3 has minor corrections and improvements. Final submitted version
Journal: Acta Math. 202 (2009), no. 2, 195--239
Cobordism categories of manifolds with corners
The homotopy type of the polyhedral product for shifted complexes
Homotopy types of $SU(n)$-gauge groups over non-spin 4-manifolds
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