Knots with Hopf crossing number at most one
Geometric Topology
2020-06-25 v1
Abstract
We consider diagrams of links in obtained by projection from with the Hopf map and the minimal crossing number for such diagrams. Knots admitting diagrams with at most one crossing are classified. Some properties of these knots are exhibited. In particular, we establish which of these knots are algebraic and, for such knots, give an answer to a problem posed by Fiedler.
Cite
@article{arxiv.1907.11614,
title = {Knots with Hopf crossing number at most one},
author = {Maciej Mroczkowski},
journal= {arXiv preprint arXiv:1907.11614},
year = {2020}
}
Comments
25 pages, 9 figures, accepted to be published in the Osaka Journal of Mathematics