Cobordism Categories and their Classifying Spaces
I will report on recent work with Ib Madsen, Soren Galatius, and Michael Weiss in
which we show that the cobordism category of d - 1 dimensional closed, compact
manifolds and their d dimensional cobordisms is the inﬁnite loop space associated to
the spectrum MOd shifted by d - 1 dimensions. There is a similar theorem in the
This work was motivated by the case d = 2 which plays an important role in
topological conformal ﬁeld theory and recently led to the proof of the Mumford
conjecture by Madsen and Weiss.