Core curves of triangulated solid tori
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- by Marc Lackenby PDF
- Trans. Amer. Math. Soc. 366 (2014), 6027-6050
Abstract:
We show that in any triangulation of a solid torus there is a pre-core curve that lies in the 2-skeleton and that intersects the interior of each face in at most 10 straight arcs. By definition, a pre-core curve is a simple closed curve that becomes a core curve when a collar is attached to the boundary of the solid torus. This theorem imposes restrictions on the possible Riemannian metrics on a solid torus. It also has applications in knot theory.References
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Additional Information
- Marc Lackenby
- Affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, United Kingdom
- Received by editor(s): February 2, 2012
- Received by editor(s) in revised form: March 19, 2013
- Published electronically: June 30, 2014
- © Copyright 2014 by the author
- Journal: Trans. Amer. Math. Soc. 366 (2014), 6027-6050
- MSC (2010): Primary 57N10
- DOI: https://doi.org/10.1090/S0002-9947-2014-06170-9
- MathSciNet review: 3256192