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2005 Complements of tori and Klein bottles in the 4–sphere that have hyperbolic structure
Dubravko Ivanšić, John G Ratcliffe, Steven T Tschantz
Algebr. Geom. Topol. 5(3): 999-1026 (2005). DOI: 10.2140/agt.2005.5.999


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 Ivanšić. John G Ratcliffe. Steven T Tschantz. "Complements of tori and Klein bottles in the 4–sphere that have hyperbolic structure." Algebr. Geom. Topol. 5 (3) 999 - 1026, 2005.


Received: 1 March 2005; Revised: 28 June 2005; Accepted: 18 July 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1085.57013
MathSciNet: MR2171801
Digital Object Identifier: 10.2140/agt.2005.5.999

Primary: 57M50 , 57Q45

Keywords: hyperbolic 4–manifolds , links in simply-connected closed 4–manifolds , links in the 4–sphere

Rights: Copyright © 2005 Mathematical Sciences Publishers


Vol.5 • No. 3 • 2005
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