Path-component invariants for spaces of positive scalar curvature   metrics
  The Kreck-Stolz $s$-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being defined only under restrictive topological conditions. The aim of this paper is to construct an analogous invariant for certain product manifolds on which the $s$-invariant is not defined. 
David J. Wraith
math.DG