Volume 8, issue 2 (2008)

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A remarkable DGmodule model for configuration spaces

Pascal Lambrechts and Don Stanley

Algebraic & Geometric Topology 8 (2008) 1191–1222

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 Σk–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.

Poincaré duality, Lefschetz duality, Sullivan model, configuration spaces
Mathematical Subject Classification 2000
Primary: 55P62, 55R80
Received: 17 July 2007
Revised: 19 March 2008
Accepted: 20 May 2008
Published: 26 July 2008
Pascal Lambrechts
Chercheur qualifié au FNRS
Université Catholique de Louvain
Institut Mathématique
Chemin du Cyclotron, 2
B-1348 Louvain-la-Neuve
Don Stanley
University of Regina
Department of Mathematics
College West 307.14
Regina, Saskatchewan
S4S 0A2