Browsing by Subject "POLYNOMIALS"

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    Obstructions to Lagrangian concordance
    (Algebraic & Geometric Topology, 2016-04-26) Cornwell, Christopher; Ng, Lenhard; Sivek, Steven
    We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in $\mathbb{R}^3$. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with non-reversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to 14 crossings that have Legendrian representatives that are Lagrangian slice.
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    ON ARC INDEX AND MAXIMAL THURSTON–BENNEQUIN NUMBER
    (Journal of Knot Theory and Its Ramifications, 2012-04) Ng, L
    We discuss the relation between arc index, maximal ThurstonBennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal ThurstonBennequin number for all knots with at most 11 crossings. For some of these knots, the calculation requires a consideration of cables which also allows us to compute the maximal self-linking number for all knots with at most 11 crossings. © 2012 World Scientific Publishing Company.