Volume 4, issue 2 (2004)

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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

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 2000
Primary: 55R80
Secondary: 57Q35, 55R70
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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