The homotopy type of the cobordism category

Abstract

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.

40 pages. v2 has improved notation, added explanations, and minor mistakes fixed. v3 has minor corrections and improvements. Final submitted version

References in corpus (1)

• Homological stability for the mapping class groups of non-orientable surfaces

Cited by in corpus (2)

• Homological stability for the mapping class groups of non-orientable surfaces
• Dimension vs. Genus: A surface realization of the little k-cubes and an E_{\infty}-operad