Knot Graphs and Gromov Hyperbolicity
Abstract
We define a broad class of graphs that generalize the Gordian graph of knots. These knot graphs take into account unknotting operations, the concordance relation, and equivalence relations generated by knot invariants. We prove that overwhelmingly, the knot graphs are not Gromov hyperbolic, with the exception of a particular family of quotient knot graphs. We also investigate the property of homogeneity, and prove that the concordance knot graph is homogeneous. Finally, we prove that that for any , there exists a knot such that the ball of radius in the Gordian graph centered at contains no connected sum of torus knots.
Keywords
Cite
@article{arxiv.1912.03766,
title = {Knot Graphs and Gromov Hyperbolicity},
author = {Stanislav Jabuka and Beibei Liu and Allison H. Moore},
journal= {arXiv preprint arXiv:1912.03766},
year = {2021}
}
Comments
23 pages, 5 figures. Major restructuring of the article and exposition. This version similar to the one accepted by Mathematische Zeitschrift