On the deleted squares of lens spaces

Abstract

The configuration space F2(M ) of ordered pairs of distinct points in a manifold M , also known as the deleted square of M , is not a homotopy invariant of M : Longoni and Salvatore produced examples of homotopy equivalent lens spaces M and N of dimension three for which F2(M ) and F2(N ) are not homotopy equivalent. In this paper, we study the natural question whether two arbitrary 3-dimensional lens spaces M and N must be homeomorphic in order for F2(M ) and F2(N ) to be homotopy equivalent. Among our tools are the Cheeger-Simons differential characters of deleted squares and the Massey products of their universal covers.