Introduction to Graph-Link Theory
Geometric Topology
2008-10-31 v1 Combinatorics
Abstract
The present paper is an introduction to a combinatorial theory arising as a natural generalisation of classical and virtual knot theory. There is a way to encode links by a class of `realisable' graphs. When passing to generic graphs with the same equivalence relations we get `graph-links'. On one hand graph-links generalise the notion of virtual link, on the other hand they do not feel link mutations. We define the Jones polynomial for graph-links and prove its invariance. We also prove some a generalisation of the Kauffman-Murasugi-Thistlethwaite theorem on `minmal diagrams' for graph-links
Cite
@article{arxiv.0810.5522,
title = {Introduction to Graph-Link Theory},
author = {Denis P. Ilyutko and Vassily O. Manturov},
journal= {arXiv preprint arXiv:0810.5522},
year = {2008}
}
Comments
34 pages, 14 figures