A remarkable DGmodule model for configuration spaces

Lambrechts, Pascal; Stanley, Don

doi:10.2140/agt.2008.8.1191

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A remarkable DGmodule model for configuration spaces

Pascal Lambrechts and Don Stanley

Algebraic & Geometric Topology 8 (2008) 1191–1222

DOI: 10.2140/agt.2008.8.1191

Abstract

Let $M$ be a simply connected closed manifold and consider the (ordered) configuration space $F (M, k)$ of $k$ points in $M$ . In this paper we construct a commutative differential graded algebra which is a potential candidate for a model of the rational homotopy type of $F (M, k)$ . We prove that our model it is at least a $Σ_{k}$ –equivariant differential graded model.

We also study Lefschetz duality at the level of cochains and describe equivariant models of the complement of a union of polyhedra in a closed manifold.

Keywords

Poincaré duality, Lefschetz duality, Sullivan model, configuration spaces

Mathematical Subject Classification 2000

Primary: 55P62, 55R80

References

Publication

Received: 17 July 2007

Revised: 19 March 2008

Accepted: 20 May 2008

Published: 26 July 2008

Authors

Pascal Lambrechts
Chercheur qualifié au FNRS Université Catholique de Louvain Institut Mathématique Chemin du Cyclotron, 2 B-1348 Louvain-la-Neuve BELGIUM
http://milnor.math.ucl.ac.be/plwiki/PascalLambrechtsProfessional/HomePage
Don Stanley
University of Regina Department of Mathematics College West 307.14 Regina, Saskatchewan S4S 0A2 Canada

Volume 8, issue 2 (2008)