A model for configuration spaces of points

Campos, Ricardo; Willwacher, Thomas

doi:10.2140/agt.2023.23.2029

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A model for configuration spaces of points

Ricardo Campos and Thomas Willwacher

Algebraic & Geometric Topology 23 (2023) 2029–2106

DOI: 10.2140/agt.2023.23.2029

Abstract

We construct a real combinatorial model for the configuration spaces of points of compact smooth oriented manifolds without boundary. We use these models to show that the real homotopy type of configuration spaces of a simply connected such manifold only depends on the real homotopy type of the manifold.

Moreover, we show that for framed $D$ –dimensional manifolds these models capture a natural right homotopy action of the little $D$ –disks operad.

Keywords

operads, configurations spaces, rational homotopy theory, embedding calculus, factorization homology

Mathematical Subject Classification

Primary: 55P62, 81Q30

Secondary: 16E45, 18M60, 18N40, 53C15

References

Publication

Received: 3 September 2020

Revised: 20 September 2021

Accepted: 19 December 2021

Published: 25 July 2023

Authors

Ricardo Campos
University of Montpellier Montpellier France

Thomas Willwacher
Department of Mathematics ETH Zurich Zurich Switzerland

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Volume 23, issue 5 (2023)