  Many noncompact hyperbolic 3-manifolds are topologically complements of links
in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of
noncompact hyperbolic 4-manifolds, all of which are topologically complements
of varying numbers of tori and Klein bottles in the 4-sphere. Finite covers of
some of those manifolds are then shown to be complements of tori and Klein
bottles in other simply-connected closed 4-manifolds. All the examples are
based on a construction of Ratcliffe and Tschantz, who produced 1171 noncompact
hyperbolic 4-manifolds of minimal volume. Our examples are finite covers of
some of those manifolds.
