Geodesic
A remarkable DGmodule model for configuration spaces
Lambrechts, Pascal1 ; Stanley, Don2
1Chercheur qualifié au FNRS, Université Catholique de Louvain, Institut Mathématique, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, BELGIUM
2University of Regina, Department of Mathematics, College West 307.14, Regina, Saskatchewan, S4S 0A2, Canada
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1191-1222
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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.

DOI : 10.2140/agt.2008.8.1191
Keywords: Poincaré duality, Lefschetz duality, Sullivan model, configuration spaces

Lambrechts, Pascal  1   ; Stanley, Don  2

1 Chercheur qualifié au FNRS, Université Catholique de Louvain, Institut Mathématique, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, BELGIUM
2 University of Regina, Department of Mathematics, College West 307.14, Regina, Saskatchewan, S4S 0A2, Canada 
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Lambrechts, Pascal; Stanley, Don. A remarkable DGmodule model for configuration spaces. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1191-1222. doi: 10.2140/agt.2008.8.1191

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