  We make use of the flexibility of infinite-index solutions to the Allen-Cahn
equation to show that, given any compact hypersurface $\Sigma$ of R^d, with
$d\geq 4$, there is a bounded entire solution of the Allen-Cahn equation on R^d
whose zero level set has a connected component diffeomorphic (and arbitrarily
close) to a rescaling of $\Sigma$. More generally, we prove the existence of
solutions with a finite number of compact connected components of prescribed
topology in their zero level sets.
