1. INTRODUCTION TO GRAPH-LINK THEORY.
- Author
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ILYUTKO, DENIS PETROVICH and MANTUROV, VASSILY OLEGOVICH
- Subjects
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KNOT theory , *SET theory , *POLYNOMIALS , *MUTATIONS (Algebra) , *MATHEMATICAL analysis , *MATHEMATICS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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