19 research outputs found

    What is a Legendrian Knot?

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    Duality for Contact Homology of Legendrian knots

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    In this paper, I prove a beautiful symmetry property for the contact homology invariant of Legendrian knots, which are mathematical knots that satisfy an additional geometric property. In addition to its intrinsic beauty, the symmetry simplifies calculations; further, the framework developed in its proof opens up further research into the structure of the invariant. --author-supplied descriptio

    Second-order Partial Derivatives

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    Duality for Contact Homology of Legendrian knots

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    In this paper, I prove a beautiful symmetry property for the contact homology invariant of Legendrian knots, which are mathematical knots that satisfy an additional geometric property. In addition to its intrinsic beauty, the symmetry simplifies calculations; further, the framework developed in its proof opens up further research into the structure of the invariant. --author-supplied descriptio

    Cross Sections of Graphs of Functions of Two Variables

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    The Community Math Teaching Project

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    Positive Knots and Lagrangian Fillability

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