Soren Galatius

Monoids of moduli spaces of manifolds

We study categories of d-dimensional cobordisms from the perspective of Tillmann and Galatius-Madsen-Tillmann-Weiss. There is a category

Homological stability for moduli spaces of high dimensional manifolds. I

C_\theta

Divisibility of the stable Miller-Morita-Mumford classes

of closed smooth (d-1)-manifolds and smooth d-dimensional cobordisms, equipped with generalised orientations specified by a fibration

Derived Galois deformation rings

\theta : X \to BO(d)

Tautological rings for high dimensional manifolds

. The main result of GMTW is a determination of the homotopy type of the classifying space

Algebraic Topology: Applications and New Directions

BC_\theta

Secondary characteristic classes of surface bundles

. The goal of the present paper is a systematic investigation of subcategories

The homotopy type of the cobordism category

D

Stable homology of automorphism groups of free groups

of

Mod p homology of the stable mapping class group

C_\theta