One-point compactifications of configuration spaces and the self duality of the little disks operad

Malin, Connor

doi:10.2140/agt.2025.25.4163

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One-point compactifications of configuration spaces and the self duality of the little disks operad

Connor Malin

Algebraic & Geometric Topology 25 (2025) 4163–4184

DOI: 10.2140/agt.2025.25.4163

Abstract

Using configuration space level Pontryagin–Thom constructions, we construct a simple Koszul self duality map for the little disks operad $Σ_{+}^{\infty} E_{n}$ . For a framed $n$ -manifold $M$ , we show that a compatible self duality map exists for $Σ_{+}^{\infty} E_{M}$ .

Keywords

Koszul duality, operads, little disks operad, $E_{n}$ operad, spectra, configuration spaces

Mathematical Subject Classification

Primary: 18M70, 55M05, 55P42

References

Publication

Received: 13 January 2024

Revised: 7 August 2024

Accepted: 15 September 2024

Published: 29 October 2025

Authors

Connor Malin
Max Planck Institute for Mathematics Bonn Germany

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Volume 25, issue 7 (2025)