The rational homotopy type of configuration spaces of two points
[Le type d'homotopie rationnel des espaces de configuration de deux points]
Lambrechts, Pascal1 ; Stanley, Don
1 Université de Louvain, Institut Mathématique, 2 chemin du Cyclotron, 1348 Louvain-la-Neuve, (Belgique), University of Ottawa, Department of Mathematics and Statistics, 585 King Edward Ave., Ottawa, ON K1N 6N5 (CANADA)
Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1029-1052.

Nous démontrons que le type d’homotopie rationnelle de l’espace des configurations de deux points dans une variété fermée 2-connexe dépend uniquement du type d’homotopie rationnelle de cette variété et nous montrons comment construire un modèle de Sullivan de cet espace de configuration. Nous étudions aussi la formalité des espaces de configuration.

We prove that the rational homotopy type of the configuration space of two points in a 2-connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.

DOI : 10.5802/aif.2042
Classification : 55P62
Keywords: configuration space, Sullivan model
Mot clés : espaces de configuration, modèles de Sullivan
Lambrechts, Pascal 1 ; Stanley, Don 

1 Université de Louvain, Institut Mathématique, 2 chemin du Cyclotron, 1348 Louvain-la-Neuve, (Belgique), University of Ottawa, Department of Mathematics and Statistics, 585 King Edward Ave., Ottawa, ON K1N 6N5 (CANADA) 
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Lambrechts, Pascal; Stanley, Don. The rational homotopy type of configuration spaces of two points. Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1029-1052. doi : 10.5802/aif.2042. https://numdam.org/articles/10.5802/aif.2042/

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