  We prove that, given any knot $\gamma$ in a compact 3-manifold M, there
exists a Riemannian metric on M such that there is a complex-valued
eigenfunction u of the Laplacian, corresponding to the first nontrivial
eigenvalue, whose nodal set $u^{-1}(0)$ has a connected component given by
$\gamma$. Higher dimensional analogs of this result will also be considered.
