On a move reducing the genus of a knot diagram
Geometric Topology
2013-06-17 v2 Combinatorics
Abstract
For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this operation to certainly decrease the genus. The proof involves the study of a relation between the genus of a virtual knot diagram and the genus of a knotoid diagram, the former of which has been introduced by Stoimenow, Tchernov and Vdovina, and the latter by Turaev recently. Our operation has a simple interpretation in terms of Gauss codes and hence can easily be computer-implemented.
Keywords
Cite
@article{arxiv.1111.3215,
title = {On a move reducing the genus of a knot diagram},
author = {Kenji Daikoku and Keiichi Sakai and Masamichi Takase},
journal= {arXiv preprint arXiv:1111.3215},
year = {2013}
}
Comments
12 pages, 12 figures, to appear in Indiana University Mathematics Journal