#### 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

## Archival Version

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