  We study the geodesic distance induced by right-invariant metrics on the
group $\operatorname{Diff}_c(M)$ of compactly supported diffeomorphisms of a
manifold $M$, and show that it vanishes for the critical Sobolev norms
$W^{s,n/s}$, where $n$ is the dimension of $M$ and $s\in(0,1)$. This completes
the proof that the geodesic distance induced by $W^{s,p}$ vanishes if $sp\le n$
and $s<1$, and is positive otherwise. The proof is achieved by combining the
techniques of two recent papers --- [JM19] by the authors, which treated the
sub-critical case, and [BHP18] of Bauer, Harms and Preston, which treated the
critical 1-dimensional case.
