The minimum crossing number of essential tangles
Geometric Topology
2017-08-30 v2
Abstract
In this paper we compute the sharp lower bounds for the crossing number of -string -loop essential tangles. For essential tangles with only string components, we characterise the ones with the minimum crossing number for a given number of components, both when the tangle has knotted strings or only unknotted strings.
Cite
@article{arxiv.1505.07268,
title = {The minimum crossing number of essential tangles},
author = {João Miguel Nogueira and António Salgueiro},
journal= {arXiv preprint arXiv:1505.07268},
year = {2017}
}
Comments
16 pages, 20 figures; In this version we correct three arguments on the proofs of the tangles of Theorems 1.1 and 1.2 being essential. The results of the original paper remain unaltered