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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Homological stability for moduli spaces of high dimensional manifolds. I
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by Søren Galatius and Oscar Randal-Williams HTML | PDF
J. Amer. Math. Soc. 31 (2018), 215-264 Request permission

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
  • Email: galatius@stanford.edu
  • Oscar Randal-Williams
  • Affiliation: Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
  • MR Author ID: 852236
  • Email: o.randal-williams@dpmms.cam.ac.uk
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 31 (2018), 215-264
  • MSC (2010): Primary 57R90; Secondary 57R15, 57R56, 55P47
  • DOI: https://doi.org/10.1090/jams/884
  • MathSciNet review: 3718454