Configuration spaces as commutative monoids
Accepted version
Peer-reviewed
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Authors
Randal-Williams, Oscar 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
1469-2120
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Publisher
Wiley
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Sponsorship
European Union’s Horizon 2020 research and innovation programme (grant agreement No. 756444).