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ON A GENERALIZATION OF THE ALEXANDER POLYNOMIAL FOR LONG VIRTUAL KNOTS

DENIS AFANASIEV

Moscow State University, Main Building, Chair of Differential Geometry and Applications, Moscow Leninskie Gory, 1, 119991, Russia

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https://doi.org/10.1142/S021821650900752XCited by:5 (Source: Crossref)

Abstract

We construct a new invariant polynomial for long virtual knots. It is a generalization of the Alexander polynomial. We designate it as ζ by meaning an analogy with ζ-polynomial for virtual links. The degree of ζ-polynomial estimates the virtual crossing number. We describe some application of ζ-polynomial for the study of minimal long virtual diagrams with respect to the number of virtual crossings.

Keywords:

AMSC: 57M25

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