March 15th, 2007

Soren Galatius (Stanford)

Title: The Homotopy Type of the Cobordism Category

Abstract: The d-dimensional cobordism category C_d has closed (d-1)-dimensional manifolds as objects and compact d-dimensional cobordisms as morphisms. Thom's theorem determines pi_0 of the classifying space BC_d. I will discuss joint work with Madsen, Tillmann and Weiss, in which we determine the homotopy type of BC_d. As a corollary we get a new proof of Madsen-Weiss' generalized Mumford conjecture. arXiv: math.AT/0605249.