Homological stability for moduli spaces of high dimensional manifolds

TL;DR

This paper proves a homological stability theorem for moduli spaces of high-dimensional manifolds, extending classical results and enabling calculations of their homology in certain degrees.

Contribution

It generalizes Harer's stability theorem to high-dimensional manifolds and provides new homology calculations for their moduli spaces.

Findings

Homological stability holds for moduli spaces of g(S^n x S^n) when n > 2.

The results extend classical stability theorems to high-dimensional cases.

Homology of these moduli spaces can be explicitly computed in certain degree ranges.

Abstract

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of these moduli spaces in a range of degrees.