%0 Journal Article
%T Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure
%A Dubravko Ivansic
%A John G. Ratcliffe
%A Steven T. Tschantz
%J Mathematics
%D 2005
%I arXiv
%R 10.2140/agt.2005.5.999
%X 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.
%U http://arxiv.org/abs/math/0502293v2