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May 2008 Totally geodesic Seifert surfaces in hyperbolic knot and link complements, II
C. Adams, H. Bennett, C. Davis, M. Jennings, J. Kloke, N. Perry, E. Schoenfeld
J. Differential Geom. 79(1): 1-23 (May 2008). DOI: 10.4310/jdg/1207834655

Abstract

We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.

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C. Adams. H. Bennett. C. Davis. M. Jennings. J. Kloke. N. Perry. E. Schoenfeld. "Totally geodesic Seifert surfaces in hyperbolic knot and link complements, II." J. Differential Geom. 79 (1) 1 - 23, May 2008. https://doi.org/10.4310/jdg/1207834655

Information

Published: May 2008
First available in Project Euclid: 10 April 2008

zbMATH: 1158.57004
MathSciNet: MR2414747
Digital Object Identifier: 10.4310/jdg/1207834655

Rights: Copyright © 2008 Lehigh University

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Vol.79 • No. 1 • May 2008
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