Algebraic and Geometric Topology 5 (2005), paper no. 41, pages 999-1026.

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

Dubravko Ivansic, John G. Ratcliffe and Steven T. Tschantz

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.

Keywords. Hyperbolic 4-manifolds, links in the 4-sphere, links in simply-connected closed 4-manifolds

AMS subject classification. Primary: 57M50, 57Q45.

E-print: arXiv:math.GT/0502293

DOI: 10.2140/agt.2005.5.999

Submitted: 1 March 2005. (Revised: 28 June 2005.) Accepted: 18 July 2005. Published: 18 August 2005.

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Dubravko Ivansic, John G. Ratcliffe and Steven T. Tschantz
DI: Department of Mathematics and Statistics
Murray State University, Murray, KY 42071, USA

JR and ST: Department of Mathematics, Vanderbilt University
Nashville, TN 37240, USA

Email: dubravko.ivansic@murraystate.edu, ratclifj@math.vanderbilt.edu, tschantz@math.vanderbilt.edu

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