Link diagrams with low Turaev genus
Geometric Topology
2015-12-01 v2
Abstract
We classify link diagrams with Turaev genus one and two in terms of an alternating tangle structure of the link diagram. The proof involves surgery along simple closed curves on the Turaev surface, called cutting loops, which have corresponding cutting arcs that are visible on the planar link diagram. These also provide new obstructions for a link diagram on a surface to come from the Turaev surface algorithm.
Cite
@article{arxiv.1507.02918,
title = {Link diagrams with low Turaev genus},
author = {Seungwon Kim},
journal= {arXiv preprint arXiv:1507.02918},
year = {2015}
}
Comments
21 pages, 35 figures