Geodesic
Complements of tori and Klein bottles in the 4–sphere that have hyperbolic structure
Ivanšić, Dubravko1 ; Ratcliffe, John G2 ; Tschantz, Steven T2
1Department of Mathematics and Statistics, Murray State University, Murray KY 42071, USA
2Department of Mathematics, Vanderbilt University, Nashville TN 37240, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 999-1026
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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.

DOI : 10.2140/agt.2005.5.999
Keywords: hyperbolic 4–manifolds, links in the 4–sphere, links in simply-connected closed 4–manifolds

Ivanšić, Dubravko  1   ; Ratcliffe, John G  2   ; Tschantz, Steven T  2

1 Department of Mathematics and Statistics, Murray State University, Murray KY 42071, USA
2 Department of Mathematics, Vanderbilt University, Nashville TN 37240, USA 
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Ivanšić, Dubravko; Ratcliffe, John G; Tschantz, Steven T. Complements of tori and Klein bottles in the 4–sphere that have hyperbolic structure. Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 999-1026. doi: 10.2140/agt.2005.5.999

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