Browsing by Subject "CONTACT HOMOLOGY"

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    Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra
    (Algebraic & Geometric Topology, 2013-08-01) Ng, L; Rutherford, D
    We develop a close relation between satellites of Legendrian knots in ℝ3and the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a Legendrian knot in ℝ3and augmentations of its DGA by showing that the DGA has finite-dimensional representations if and only if there exist certain rulings of satellites of the knot. We derive several consequences of this result, notably that the question of existence of ungraded finite-dimensional representations for the DGA of a Legendrian knot depends only on the topological type and Thurston-Bennequin number of the knot.
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    The cardinality of the augmentation category of a Legendrian link
    (Mathematical Research Letters, 2017) Ng, L; Rutherford, D; Shende, V; Sivek, S
    We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R3. This ℓhomotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We present an application to the augmentation category of doubly Lagrangian slice knots.