  We prove the existence of elements of infinite order in the homotopy groups
of the spaces $\mathcal{R}_{Ric>0}(M)$ and $\mathcal{R}_{sec>0}(M)$ of positive
Ricci and positive sectional curvature, provided that $M$ is high-dimensional
and Spin, admits such a metric and has a non-vanishing rational Pontryagin
class.
