Diffeomorphisms and positive curvature

Abstract: In this note we prove the existence of elements of infinite order in some homotopy groups of the spaces of positive Ricci and positive sectional curvature, provided that $M$ admits such a metric, is high-dimensional and has a nontrivial Pontryagin class.

Yes, there is a typo: At 5:13 I say k≥1 and write k≥0. The correct thing is k≥1.