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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Core curves of triangulated solid tori


Author: Marc Lackenby
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 57N10
Published electronically: June 30, 2014
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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.


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Additional Information

Marc Lackenby
Affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06170-9
PII: S 0002-9947(2014)06170-9
Received by editor(s): February 2, 2012
Received by editor(s) in revised form: March 19, 2013
Published electronically: June 30, 2014
Article copyright: © Copyright 2014 by the author