Vertex distortion detects the unknot

Publication Date

10-1-2022

Document Type

Article

Publication Title

Journal of Knot Theory and its Ramifications

Volume

31

Issue

11

DOI

10.1142/S0218216522500742

Abstract

The first two authors introduced vertex distortion of lattice knots and showed that the vertex distortion of the unknot is 1. It was conjectured that the vertex distortion of a knot class is 1 if and only if it is trivial. We use Denne and Sullivan's lower bound on Gromov distortion to bound the vertex distortion of non-trivial lattice knots. This bounding allows us to conclude that a knot class has vertex distortion 1 if and only if it is trivial. We also show that vertex distortion does not have a universal upper bound and provide a vertex distortion calculator.

Keywords

distortion, Lattice knots

Department

Mathematics and Statistics

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