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Totally geodesic boundaries of knot complements


Author: Richard P. Kent IV
Journal: Proc. Amer. Math. Soc. 133 (2005), 3735-3744
MSC (2000): Primary 57M50
DOI: https://doi.org/10.1090/S0002-9939-05-07969-4
Published electronically: June 8, 2005
MathSciNet review: 2163613
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a compact orientable $3$-manifold $M$ whose boundary is a hyperbolic surface and a simple closed curve $C$ in its boundary, every knot in $M$ is homotopic to one whose complement admits a complete hyperbolic structure with totally geodesic boundary in which the geodesic representative of $C$ is as small as you like.


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Additional Information

Richard P. Kent IV
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: rkent@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9939-05-07969-4
Received by editor(s): May 12, 2004
Received by editor(s) in revised form: August 7, 2004
Published electronically: June 8, 2005
Additional Notes: This work was supported in part by a University of Texas Continuing Fellowship.
Dedicated: for Kimberly
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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