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A model for configuration spaces of points

Ricardo Campos and Thomas Willwacher

Algebraic & Geometric Topology 23 (2023) 2029–2106
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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