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Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure

Dubravko Ivansic·John G. Ratcliffe·Steven T. Tschantz
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Abstract

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.

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Dubravko Ivansic, John G. Ratcliffe, Steven T. Tschantz. 2005-08-24. Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure. https://doi.org/10.2140/agt.2005.5.999

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