Maximal Thurston-Bennequin Number of Two-Bridge Links

By Lenhard L. Ng. 2000

47 citations recorded by the source corpus.

We compute the maximal Thurston-Bennequin number for a Legendrian two-bridge knot or oriented two-bridge link in standard con- tact R 3 , by showing that the upper bound given by the Kauman polyno- mial is sharp. As an application, we present a table of maximal Thurston- Bennequin numbers for prime knots with nine or fewer crossings. AMS Classication 53D12; 57M15

Subfields: Atomic and Molecular Physics, and Optics, Genetics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bae51405c0a5b495cedefdec82afc9dc4a87fa06

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

A concordance invariant from the Floer homology of double branched covers (2005, background): “The results of Livingston and Naik from [18], together with the fact that the Thurston-Bennequin number TB(K1) = 2m− 1 is positive (see for example [30]), imply that τ(Wh(K1)) = s (Wh(K1)) = 1.”
NOTIONS OF POSITIVITY AND THE OZSVÁTH–SZABÓ CONCORDANCE INVARIANT (2005, background): “In [28], Plamenvskaya showed that TB(K) ≤ 2τ(K)− 1 and hence any knot for which this fails to be equality will provide a counterexample to the theorem above if the fiberedness condition on K is removed (an example of such a knot is the figure-8, see [18]).”
A Legendrian Thurston-Bennequin bound from Khovanov homology (2005, background): “It is sharp for all knots with 9 or fewer crossings, and in particular resolves the one unknown value in the table of tb from [17].”
Legendrian and transverse twist knots (2010, background): “ For twist knots, Proposition 2.5 allows easy calculation of the maximal value of tb; we note that the following result can also be derived from the more general calculation for two-bridge knots from [19]. Proposition 2.6. The maximal Thurston–Bennequin number for Km is: tb(Km) = −m−1 m≥ 0 ”
Legendrian and Transversal Knots (2003, background): “In this section we discuss Ng’s description of the DGA in the front projection [75].”