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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Legendrian framings for two-bridge links


Authors: Sebastian Baader and Masaharu Ishikawa
Journal: Proc. Amer. Math. Soc. 139 (2011), 4513-4520
MSC (2010): Primary 57M27
Published electronically: April 4, 2011
MathSciNet review: 2823096
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Abstract: We define the Thurston-Bennequin polytope of a two-component link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive surfaces in $ \mathbb{R}^3$ all of whose sub-annuli are quasipositive.


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Additional Information

Sebastian Baader
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Email: sebastian.baader@math.unibe.ch

Masaharu Ishikawa
Affiliation: Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan
Email: ishikawa@math.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10888-8
PII: S 0002-9939(2011)10888-8
Received by editor(s): October 26, 2009
Received by editor(s) in revised form: May 7, 2010, and October 11, 2010
Published electronically: April 4, 2011
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.