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A class of index polynomial invariants for virtual knots using flat virtual knots invariants

Bingyu Lin

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

E-mail Address: linbingyu@mail.dlut.edu.cn

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and

Fengling Li

https://orcid.org/0000-0001-9670-2215

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

E-mail Address: fenglingli@dlut.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218216524500433Cited by:0 (Source: Crossref)

Abstract

In this paper, a class of indices is constructed using a polynomial invariant $g$ for flat virtual knots. For any integer $n$ not less than $2$ , the classical crossings of an oriented virtual knot diagram are classified into two types according to whether the intersection index of the classical crossings can be divided by $n$ . We assign an index to each classical crossing whose intersection index is not divisible by $n$ , the index is related to the flat virtual knot diagram corresponding to the virtual knot diagram obtained by applying 0-smoothing at that classical crossing. We construct a class of index polynomials by using these indices and prove that they are invariants of virtual knots, and also discuss some of their properties.

Keywords:

AMSC: 57K12, 57K14

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