Virtual Knot Cobordism
Geometric Topology
2014-09-02 v1
Abstract
This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots are given. Determinations of the four-ball genus of positive virtual knots are given using the results of a companion paper by the author and Heather Dye and Aaron Kaestner. Problems related to band-passing are explained, and a theory of isotopy of virtual surfaces is formulated in terms of a generalization of the Yoshikawa moves.
Keywords
Cite
@article{arxiv.1409.0324,
title = {Virtual Knot Cobordism},
author = {Louis H. Kauffman},
journal= {arXiv preprint arXiv:1409.0324},
year = {2014}
}
Comments
32 pages, 43 figures, LaTeX document