  Hopf solitons in the Skyrme-Faddeev system on $R^3$ typically have a
complicated structure, in particular when the Hopf number Q is large. By
contrast, if we work on a compact 3-manifold M, and the energy functional
consists only of the Skyrme term (the strong-coupling limit), then the picture
simplifies. There is a topological lower bound $E\geq Q$ on the energy, and the
local minima of E can look simple even for large Q. The aim here is to describe
and investigate some of these solutions, when M is $S^3$, $T^3$ or $S^2 \times
S^1$. In addition, we review the more elementary baby-Skyrme system, with M
being $S^2$ or $T^2$.
