Title: On the homotopy invariance of configuration spaces
Author(s): Mokhtar Aouina and John R. Klein
Author's e-mail address: aouina@math.wayne.edu, klein@math.wayne.edu
AMS classification number: Primary 55R80; Secondary 57Q35, 55R70.
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 embedding theory and fiberwise algebraic topology.