Virtual knot cobordism and bounding the slice genus
Geometric Topology
2022-10-04 v2
Abstract
In this paper, we compute the slice genus for many low-crossing virtual knots. For instance, we show that 1295 out of 92800 virtual knots with 6 or fewer crossings are slice, and that all but 248 of the rest are not slice. Key to these results are computations of Turaev's graded genus, which we show extends to give an invariant of virtual knot concordance. The graded genus is remarkably effective as a slice obstruction, and we develop an algorithm that applies virtual unknotting operations to determine the slice genus of many virtual knots with 6 or fewer crossings.
Keywords
Cite
@article{arxiv.1708.05982,
title = {Virtual knot cobordism and bounding the slice genus},
author = {Hans U. Boden and Micah Chrisman and Robin Gaudreau},
journal= {arXiv preprint arXiv:1708.05982},
year = {2022}
}
Comments
26 pages, many figures, supplementary dataset available online at https://micah46.wixsite.com/micahknots/slicegenus