Homological stability for moduli spaces of high dimensional manifolds. II

Abstract

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

arXiv comment60 pages, 4 figures. Final accepted version