Homological stability for moduli spaces of high dimensional manifolds. II

Abstract

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies of S$^\textit{n}$ X S$^\textit{n}$. Combined with previous work of the authors, we obtain an analogue of the Madsen-Weiss theorem for any simply-connected manifold of dimension 2$\textit{n}$ $\geq$ 6.