  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.
