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

Authors
  • Ivansic, Dubravko
  • Ratcliffe, John G.
  • Tschantz, Steven T.
Type
Published Article
Publication Date
Aug 24, 2005
Submission Date
Feb 14, 2005
Identifiers
DOI: 10.2140/agt.2005.5.999
arXiv ID: math/0502293
Source
arXiv
License
Unknown
External links

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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