Laura Starkston

  1. The Khovanov homology of (p,-p,q) pretzel knots.

    Authors: Laura Starkston
    Subjects: Geometric Topology
    Abstract

    The (p,-p,q) pretzel knots are one of the few classes of pretzel knots, where
    it is not known whether they are quasi-alternating. Thus we do not know that we
    can calculate the Khovanov homology simply from the Jones polynomial and knot
    signature. In this paper, we compute the Khovanov homology for (p,-p,q) pretzel
    knots for p=3,5,7,9,11 and arbitrarily large q, finding that these knots have
    thin Khovanov homology. We provide a conjecture for the general form of the
    Khovanov homology of (p,-p,q) pretzel knots.

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