Oscar Randal-Williams

Resolutions of moduli spaces and homological stability

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.

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

Homological stability for unordered configuration spaces

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

Relations among tautological classes revisited

\theta : X \to BO(d)

Infinite loop spaces and positive scalar curvature

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

The Picard group of the moduli space of r-Spin Riemann surfaces

BC_\theta

The homology of the stable nonorientable mapping class group

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

Generalised Miller–Morita–Mumford classes for block bundles and topological bundles

D

Embedded Cobordism Categories and Spaces of Submanifolds

of