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

Primary: 55P62, 55R80

References

Publication

Received: 17 July 2007
Revised: 19 March 2008
Accepted: 20 May 2008
Published: 26 July 2008

Authors