Virtual Crossing Realization
Geometric Topology
2007-05-23 v6
Abstract
We study virtual isotopy sequences with classical initial and final diagrams, asking when such a sequence can be changed into a classical isotopy sequence by replacing virtual crossings with classical crossings. An example of a sequence for which no such virtual crossing realization exists is given. A conjecture on conditions for realizability of virtual isotopy sequences is proposed, and a sufficient condition for realizability is found. The conjecture is reformulated in terms of 2-knots and knots in thickened surfaces.
Keywords
Cite
@article{arxiv.math/0303077,
title = {Virtual Crossing Realization},
author = {Sam Nelson},
journal= {arXiv preprint arXiv:math/0303077},
year = {2007}
}
Comments
21 pages, 10 figures. To appear in J. Knot Theory Ramifications. Version 6 includes revisions suggested by the reviewer