Homotopy theory of compactified moduli spaces. (Søren Galatius)


The Pontrjagin-Thom construction defines a map from the moduli space M_g of Riemann surfaces to a certain Thom spectrum, and the Madsen-Weiss theorem tells us that the map is a homology equivalence in a range. In many applications, not the moduli space M_g itself, but its compactification (the Deligne-Mumford compactification) is relevant. In this talk I will define a Thom spectrum with a natural map from the compactified moduli space, and describe progress towards a "compactified Madsen-Weiss theorem". This is joint work with Y. Eliashberg.