  Given a compact manifold $N^n \subset \mathbb{R}^\nu$, $s \ge 1$ and $1 \le p
< \infty$, we prove that the class of smooth maps on the cube with values into
$N^n$ is strongly dense in the fractional Sobolev space $W^{s, p}(Q^m; N^n)$
when $N^n$ is $\lfloor sp \rfloor$ simply connected. For $sp$ integer, we prove
weak density of smooth maps with values into $N^n$ when $N^n$ is $sp - 1$
simply connected. The proofs are based on the existence of a retraction of
$\mathbb{R}^\nu$ onto $N^n$ except for a small subset of $N^n$ and on a
pointwise estimate of fractional derivatives of composition of maps in $W^{s,
p} \cap W^{1, sp}$.
