Configuration spaces are not homotopy invariant

Riccardo Longoni, Paolo Salvatore

Published 2004-01-08Version 1

We present a counterexample to the conjecture on the homotopy invariance of configuration spaces. More precisely, we consider the lens spaces $L_{7,1}$ and $L_{7,2}$, and prove that their configuration spaces are not homotopy equivalent by showing that their universal coverings have different Massey products.