Cobordism Invariance of the Homotopy Type of the Space of Positive   Scalar Curvature Metrics
  We show that the homotopy type of the space of metrics of positive scalar curvature on a smooth manifold remains unchanged, after application of surgery in codimension at least three to the underlying manifold. This result is originally due to V. Chernysh, but remains unpublished. 
Mark Walsh
math.DG math.AT