The homotopy type of the cobordism category - Galatius, S; Madsen, I; Tillmann, U; Weiss, M (2009)
The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in [S2] 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, presented in [MW]. © 2009 Institut Mittag-Leffler.