Oliver Pechenik

  1. Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus.

    Authors: Allison Henrich, Noel MacNaughton, Sneha Narayan, Oliver Pechenik, Jennifer Townsend
    Subjects: Geometric Topology
    Abstract

    A pseudodiagram is a diagram of a knot with some crossing information
    missing. We review and expand the theory of pseudodiagrams introduced by R.
    Hanaki. We then extend this theory to the realm of virtual knots, a
    generalization of knots. In particular, we investigate how much crossing
    information must be known to conclude that a diagram is a diagram of the unknot
    (the trivializing number). We provide a table of trivializing numbers for knots
    with no more than 10 crossings, as well as an algorithm to calculate an upper
    bound on the trivializing number of any knot.

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