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.

Notes on file formats

Mokhtar Aouina, John R. Klein
Department of Mathematics, Wayne State University
Detroit, MI 48202, USA
Email: aouina@math.wayne.edu, klein@math.wayne.edu

AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.