On the Turaev genus of torus knots
Geometric Topology
2017-12-18 v1
Abstract
The Turaev genus and dealternating number of a link are two invariants that measure how far away a link is from alternating. We determine the Turaev genus of a torus knot with five or fewer strands either exactly or up to an error of at most one. We also determine the dealternating number of a torus knot with five or fewer strand up to an error of at most two. Additional bounds are given on the Turaev genus and dealternating number of torus links with five or fewer strands and on some infinite families of torus links on six strands.
Keywords
Cite
@article{arxiv.1703.02506,
title = {On the Turaev genus of torus knots},
author = {Kaitian Jin and Adam M. Lowrance and Eli Polston and Yanjie Zheng},
journal= {arXiv preprint arXiv:1703.02506},
year = {2017}
}
Comments
24 pages, 18 figures