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Vertex distortion detects the unknot
Journal
Journal of Knot Theory and its Ramifications
ISSN
02182165
Date Issued
2022-10-01
Author(s)
Campisi, Marion
Cazet, Nicholas
Crncevic, David
Fellman, Tasha
Kessler, Phillip
Rieke, Nikolas
Srivastava, Vatsal
Torres, Luis
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.
Volume
31
Publication link
Subjects