Hyperbolic structure on a complement of tori in the 4-sphere Dubravko Ivanšić

@inproceedings{Murray2003HyperbolicSO,
title={Hyperbolic structure on a complement of tori in the 4-sphere Dubravko Ivan{\vs}i{\'c}},
author={Dubravko Ivan{\vs}i{\'c} Murray},
year={2003}
}

It is well known that many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. We extend this phenomenon to dimension 4 by exhibiting an example of a noncompact hyperbolic 4-manifold that is topologically the complement of 5 tori in the 4-sphere. We also exhibit examples of hyperbolic manifolds that are complements of 5n tori in a simply-connected 4-manifold with Euler characteristic 2n. All the examples are based on a construction of Ratcli¤e and Tschantz… CONTINUE READING