Homological stability for moduli spaces of high dimensional manifolds. I

Galatius, Søren; Randal-Williams, Oscar

doi:10.1090/jams/884

Homological stability for moduli spaces of high dimensional manifolds. I
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by Søren Galatius and Oscar Randal-Williams;

J. Amer. Math. Soc. 31 (2018), 215-264

DOI: https://doi.org/10.1090/jams/884

Published electronically: June 23, 2017

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Abstract:

We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension $2n > 4$, with respect to forming connected sum with $S^n \times S^n$. This is analogous to 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 the moduli spaces of manifolds diffeomorphic to connected sums of $S^n \times S^n$ in a range of degrees.

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