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2017 Betti numbers and stability for configuration spaces via factorization homology
Ben Knudsen
Algebr. Geom. Topol. 17(5): 3137-3187 (2017). DOI: 10.2140/agt.2017.17.3137

Abstract

Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold M, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology of M. By locating the homology of each configuration space within the Chevalley–Eilenberg complex of this Lie algebra, we extend theorems of Bödigheimer, Cohen and Taylor and of Félix and Thomas, and give a new, combinatorial proof of the homological stability results of Church and Randal-Williams. Our method lends itself to explicit calculations, examples of which we include.

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Ben Knudsen. "Betti numbers and stability for configuration spaces via factorization homology." Algebr. Geom. Topol. 17 (5) 3137 - 3187, 2017. https://doi.org/10.2140/agt.2017.17.3137

Information

Received: 8 December 2016; Revised: 9 December 2016; Accepted: 25 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1377.57025
MathSciNet: MR3704255
Digital Object Identifier: 10.2140/agt.2017.17.3137

Subjects:
Primary: 57R19
Secondary: 17B56, 55R80

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 5 • 2017
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