On the homotopy invariance of configuration spaces

Aouina, Mokhtar; Klein, John R

doi:10.2140/agt.2004.4.813

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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 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

Volume 4, issue 2 (2004)