Vertex Distortion of Lattice Knots

Abstract: The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the 1-norm. We show analogous results of Gromov, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of smooth knots hold for vertex distortion, the vertex distortion of a lattice knot is 1 only if it is the unknot, and that there are minimal lattice-stick number knot conformations with arbitrarily high distortion.

algebraic topologydifferential geometrygeneral topologygeometric topology

Audience: researchers in the topic

GOATS

Series comments: Description: A series of online mini-conferences for graduate students in Geo

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