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Homological stability for moduli spaces of high dimensional manifolds. I

Authors: Søren Galatius and Oscar Randal-Williams
Journal: J. Amer. Math. Soc. 31 (2018), 215-264
MSC (2010): Primary 57R90; Secondary 57R15, 57R56, 55P47
Published electronically: June 23, 2017
MathSciNet review: 3718454
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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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Additional Information

Søren Galatius
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
ORCID: 0000-0002-1015-7322

Oscar Randal-Williams
Affiliation: Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
MR Author ID: 852236

Received by editor(s): March 23, 2016
Received by editor(s) in revised form: February 7, 2017
Published electronically: June 23, 2017
Additional Notes: The first author was partially supported by NSF grants DMS-1105058 and DMS-1405001, and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 682922).
The second author was supported by EPSRC grant EP/M027783/1 and the Herchel Smith Fund.
Both authors were supported by ERC Advanced Grant No. 228082, and the Danish National Research Foundation through the Centre for Symmetry and Deformation.
Dedicated: Dedicated to Ulrike Tillmann
Article copyright: © Copyright 2017 American Mathematical Society