Legendrian framings for two-bridge links

Baader, Sebastian; Ishikawa, Masaharu

doi:10.1090/S0002-9939-2011-10888-8

Legendrian framings for two-bridge links
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by Sebastian Baader and Masaharu Ishikawa

Proc. Amer. Math. Soc. 139 (2011), 4513-4520

DOI: https://doi.org/10.1090/S0002-9939-2011-10888-8

Published electronically: April 4, 2011

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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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