Journal of Differential Geometry

Totally geodesic Seifert surfaces in hyperbolic knot and link complements, II

C. Adams, H. Bennett, C. Davis, M. Jennings, J. Kloke, N. Perry, and E. Schoenfeld

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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.

Article information

Source
J. Differential Geom., Volume 79, Number 1 (2008), 1-23.

Dates
First available in Project Euclid: 10 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1207834655

Digital Object Identifier
doi:10.4310/jdg/1207834655

Mathematical Reviews number (MathSciNet)
MR2414747

Zentralblatt MATH identifier
1158.57004

Citation

Adams, C.; Bennett, H.; Davis, C.; Jennings, M.; Kloke, J.; Perry, N.; Schoenfeld, E. Totally geodesic Seifert surfaces in hyperbolic knot and link complements, II. J. Differential Geom. 79 (2008), no. 1, 1--23. doi:10.4310/jdg/1207834655. https://projecteuclid.org/euclid.jdg/1207834655


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