Highly twisted plat diagrams
Geometric Topology
2021-11-30 v1
Abstract
We prove that the knots and links in the infinite set of -highly twisted -plats, with , are all hyperbolic. This should be compared with a result of Futer-Purcell for -highly twisted diagrams. While their proof uses geometric methods our proof is achieved by showing that the complements of such knots or links are unannular and atoroidal. This is done by using a new approach involving an Euler characteristic argument.
Cite
@article{arxiv.2111.14231,
title = {Highly twisted plat diagrams},
author = {Nir Lazarovich and Yoav Moriah and Tali Pinsky},
journal= {arXiv preprint arXiv:2111.14231},
year = {2021}
}