Unexpected Essential Surfaces among Exteriors of Twisted Torus Knots
Geometric Topology
2023-03-22 v3
Abstract
The twisted torus knots K(p, q; r, s) are obtained by performing a sequence of s full twists on r adjacent strands of (p, q)-torus knots. Morimoto asked whether all twisted torus knots with essential tori in the exterior fit into one of two families. We prove that the answer to this question is no, by finding two different new families of toroidal twisted torus knots.
Cite
@article{arxiv.2012.09599,
title = {Unexpected Essential Surfaces among Exteriors of Twisted Torus Knots},
author = {Thiago de Paiva},
journal= {arXiv preprint arXiv:2012.09599},
year = {2023}
}
Comments
15 pages, 11 figures. v3 contains minor revisions. To appear in Algebraic & Geometric Topology