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July 2017 Homological stability for moduli spaces of high dimensional manifolds. II
Søren Galatius, Oscar Randal-Williams
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Ann. of Math. (2) 186(1): 127-204 (July 2017). DOI: 10.4007/annals.2017.186.1.4

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 $2n \ge 6$.

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Søren Galatius. Oscar Randal-Williams. "Homological stability for moduli spaces of high dimensional manifolds. II." Ann. of Math. (2) 186 (1) 127 - 204, July 2017. https://doi.org/10.4007/annals.2017.186.1.4

Information

Published: July 2017
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2017.186.1.4

Subjects:
Primary: 55P47 , 57R15 , 57R56 , 57R90

Keywords: characteristic classes , diffeomorphism groups , homological stability , moduli spaces

Rights: Copyright © 2017 Department of Mathematics, Princeton University

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Vol.186 • No. 1 • July 2017
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