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Configuration spaces as commutative monoids

Accepted version
Peer-reviewed

Type

Article

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Authors

Randal-Williams, Oscar  ORCID logo  https://orcid.org/0000-0002-7479-2878

Abstract

After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative monoid object. Using this presentation, one can quickly deduce Knudsen's formula for the rational cohomology of configuration spaces, prove rational homological stability, and understand how automorphisms of the manifold act on the cohomology of configuration spaces. Similar considerations reproduce the work of Farb--Wolfson--Wood on homological densities.

Description

Keywords

math.AT, math.AT, 55R80

Journal Title

Bulletin of the London Mathematical Society

Conference Name

Journal ISSN

0024-6093
1469-2120

Volume Title

Publisher

Wiley

Publisher DOI

Publisher URL

Sponsorship
European Union’s Horizon 2020 research and innovation programme (grant agreement No. 756444).