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Transactions of the American Mathematical Society

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Homological stability for the moduli spaces of products of spheres


Author: Nathan Perlmutter
Journal: Trans. Amer. Math. Soc. 368 (2016), 5197-5228
MSC (2010): Primary 55P47, 57R15, 57R19, 57R56
DOI: https://doi.org/10.1090/tran/6564
Published electronically: August 18, 2015
MathSciNet review: 3456177
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Nathan Perlmutter
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: nperlmut@uoregon.edu

DOI: https://doi.org/10.1090/tran/6564
Received by editor(s): January 25, 2014
Received by editor(s) in revised form: February 12, 2014, July 30, 2014, August 28, 2014, September 9, 2014, September 12, 2014, and September 15, 2014
Published electronically: August 18, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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