Algebraic & Geometric Topology

A remarkable DGmodule model for configuration spaces

Pascal Lambrechts and Don Stanley

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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.

Article information

Algebr. Geom. Topol., Volume 8, Number 2 (2008), 1191-1222.

Received: 17 July 2007
Revised: 19 March 2008
Accepted: 20 May 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P62: Rational homotopy theory 55R80: Discriminantal varieties, configuration spaces

Poincaré duality Lefschetz duality Sullivan model configuration spaces


Lambrechts, Pascal; Stanley, Don. A remarkable DGmodule model for configuration spaces. Algebr. Geom. Topol. 8 (2008), no. 2, 1191--1222. doi:10.2140/agt.2008.8.1191.

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