The support genus of certain Legendrian knots
Youlin Li, Jiajun Wang
TL;DR
This paper computes the support genus for specific Legendrian knots, including right-handed trefoils, and provides examples of knots with positive support genus and arbitrarily negative Thurston-Bennequin invariants, addressing an open question.
Contribution
It determines the support genus for all Legendrian right-handed trefoil knots and some others, and constructs examples with positive support genus and negative Thurston-Bennequin invariants.
Findings
Support genus computed for all Legendrian right-handed trefoil knots.
Examples of Legendrian knots with positive support genus and arbitrarily negative Thurston-Bennequin invariant.
Addresses an open question in the field.
Abstract
In this paper, the support genus of all Legendrian right handed trefoil knots and some other Legendrian knots is computed. We give examples of Legendrian knots in the three-sphere with the standard contact structure which have positive support genus with arbitrarily negative Thurston-Benniquin invariant. This answers a question in Onaran.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows