Hyperbolic Knotoids
Geometric Topology
2022-09-13 v1
Abstract
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints. A variety of knot invariants have been extended to knotoids. Here we provide definitions of hyperbolicity for both spherical and planar knotoids. We prove that the product of hyperbolic spherical knotoids is hyperbolic and the volumes add. We also determine the least volume of a rational spherical knotoid and provide various classes of hyperbolic knotoids. We also include tables of hyperbolic volumes for both spherical and planar knotoids.
Cite
@article{arxiv.2209.04556,
title = {Hyperbolic Knotoids},
author = {Colin Adams and Alexandra Bonat and Maya Chande and Joye Chen and Maxwell Jiang and Zachary Romrell and Daniel Santiago and Benjamin Shapiro and Dora Woodruff},
journal= {arXiv preprint arXiv:2209.04556},
year = {2022}
}
Comments
36 pages, 30 figures