Homological stability for the moduli spaces of products of spheres

Perlmutter, Nathan

doi:10.1090/tran/6564

Homological stability for the moduli spaces of products of spheres
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Trans. Amer. Math. Soc. 368 (2016), 5197-5228 Request permission

Abstract:

We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p - 2$. This result is analogous to recent results of S. Galatius and O. Randal-Williams regarding the homological stability for the moduli spaces of manifolds of dimension $2n > 4$ with respect to forming connected sums with $S^{n}\times S^{n}$.

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