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Hyperbolic structure on "link" complements in the 4-sphere
by
Dubravko Ivansic
The George Washington University
There are many known examples of link complements in the 3-sphere that carry a hyperbolic structure, but in one dimension higher none have yet been displayed. For this purpose, the proper generalization of a ``link'' in dimension 4 is a disjoint union of tori and Klein bottles inside a closed 4-manifold.
We prove that some of the examples of hyperbolic 4-manifolds constructed by Ratcliffe and Tschantz have orientable double covers that are complements of tori inside the 4-sphere. Furthermore, we show that they have higher-order covers that are complements of tori inside other simply connected 4-manifolds.
Date received: December 6, 2000
Copyright © 2000 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cafy-11.