Introduction to Graph-Link Theory

Details Introduction to Graph-Link Theory Introduction to Graph-Link Theory

2008-10-30

arxiv.org/abs/0810.5522v1

Mathematics

Geometric Topology

34 pages, 14 figures

Scientific paper

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

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