On the deleted squares of lens spaces

الأصل · EN

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.