#### Volume 4, issue 2 (2004)

 Download this article For screen For printing
 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
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 $F\left(M,k\right)$ of ordered $k$–tuples of distinct points in $M$. We show that a suitable iterated suspension of $F\left(M,k\right)$ 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
##### 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