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INTRODUCTION TO GRAPH-LINK THEORY

DENIS PETROVICH ILYUTKO

Department of Mechanics and Mathematics, Moscow State University, 119991, GSP-1, Moscow, Leninskiye Gory, Russia

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and

VASSILY OLEGOVICH MANTUROV

Moscow State Regional University, Chair of Geometry, Moscow, 105005, Radio St., 10a, Russia

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https://doi.org/10.1142/S0218216509007191Cited by:24 (Source: Crossref)

Abstract

The present paper is an introduction to a combinatorial theory arising as a natural generalization of classical and virtual knot theory. There is a way to encode links by a class of "realizable" graphs. When passing to generic graphs with the same equivalence relations we get "graph-links". On one hand graph-links generalize the notion of virtual link, on the other hand they do not detect link mutations. We define the Jones polynomial for graph-links and prove its invariance. We also prove some a generalization of the Kauffman–Murasugi–Thistlethwaite theorem on "minimal diagrams" for graph-links.

Keywords:

AMSC: 57M25

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