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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

On the homotopy invariance of configuration spaces

Mokhtar Aouina and John R Klein

Algebraic & Geometric Topology 4 (2004) 813–827

DOI: 10.2140/agt.2004.4.813

arXiv: math.AT/0310483

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 Poincaré embedding theory and fiberwise algebraic topology.

Keywords

configuration space, fiberwise suspension, embedding up to homotopy, Poincaré embedding

Mathematical Subject Classification

Primary: 55R80

Secondary: 55R70, 57Q35

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Publication

Received: 29 January 2004
Revised: 4 July 2004
Accepted: 23 September 2004
Published: 23 September 2004

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