Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/jams/884
Published electronically: June 23, 2017
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 57R90, 57R15, 57R56, 55P47

Retrieve articles in all journals with MSC (2010): 57R90, 57R15, 57R56, 55P47


Additional Information

Søren Galatius
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: galatius@stanford.edu

Oscar Randal-Williams
Affiliation: Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
Email: o.randal-williams@dpmms.cam.ac.uk

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

American Mathematical Society