  For finitely generated groups H and G, equipped with word metrics, a
translation-like action of H on G is a free action such that each element of H
acts by a map which has finite distance from the identity map in the uniform
metric. For example, if H is a subgroup of G, then right translation by
elements of H yields a translation-like action of H on G. Whyte asked whether a
group with no translation-like action by a Baumslag-Solitar group must be
hyperbolic, where the free abelian group of rank 2 is understood to be a
Baumslag-Solitar group. We show that the converse of this conjecture is false,
and in particular the fundamental group of a closed hyperbolic 3-manifold
admits a translation-like action by the free abelian group of rank 2.
