Totally geodesic boundaries of knot complements
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- by Richard P. Kent IV PDF
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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.References
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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
- 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.
- Communicated by: Ronald A. Fintushel
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3735-3744
- MSC (2000): Primary 57M50
- DOI: https://doi.org/10.1090/S0002-9939-05-07969-4
- MathSciNet review: 2163613
Dedicated: for Kimberly