Algebraic and Geometric Topology 4 (2004), paper no. 35, pages 813-827.

On the homotopy invariance of configuration spaces

Mokhtar Aouina, John R. Klein

Abstract. For a closed PL manifold M, we consider the configuration space F(M,k) of ordered k-tuples of distinct points in M. We show that a suitable iterated suspension of F(M,k) is a homotopy invariant of M. The number of suspensions we require depends on three parameters: the number of points k, the dimension of M and the connectivity of M. Our proof uses a mixture of Poincare embedding theory and fiberwise algebraic topology.

Keywords. Configuration space, fiberwise suspension, embedding up to homotopy, Poincare embedding

AMS subject classification. Primary: 55R80. Secondary: 57Q35, 55R70.

DOI: 10.2140/agt.2004.4.813

E-print: arXiv:math.AT/0310483

Submitted: 29 January 2004. (Revised: 4 July 2004.) Accepted: 23 September 2004. Published: 23 September 2004.

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Mokhtar Aouina, John R. Klein
Department of Mathematics, Wayne State University
Detroit, MI 48202, USA

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