2 problems

Let $M$ be a closed manifold, let $f:M\to M$ be a diffeomorphism preserving a volume form $\mu$, and let $\mathrm{Diff}^r_\mu(M)$ denote the corresponding space of $C^r$ volume-pre…

Let $M$ be a compact manifold and let $\operatorname{Diff}^r(M)$ be the space of $C^r$-diffeomorphisms, where $r\geq 1$, endowed with the $C^r$-topology. Let $\mathcal{MS}$ denote…