Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus
Geometric Topology
2011-09-20 v2
Abstract
A pseudodiagram is a diagram of a knot with some crossing information missing. We review and expand the theory of pseudodiagrams introduced by R. Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots. In particular, we investigate how much crossing information must be known to conclude that a diagram is a diagram of the unknot (the trivializing number). We also consider how much information is necessary to identify a non-trivial knot, a classical knot, or a non-classical knot. We then apply pseudodiagram theory to develop new upper bounds on unknotting number, virtual unknotting number, and genus.
Cite
@article{arxiv.0908.1981,
title = {Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus},
author = {Allison Henrich and Noel MacNaughton and Sneha Narayan and Oliver Pechenik and Jennifer Townsend},
journal= {arXiv preprint arXiv:0908.1981},
year = {2011}
}
Comments
25 pages, 18 figures, 1 table