Writhe polynomials and shell moves for virtual knots and links
| Autor: | Shin Satoh, Takuji Nakamura, Yasutaka Nakanishi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Polynomial
Pure mathematics 010102 general mathematics Geometric Topology (math.GT) 0102 computer and information sciences 01 natural sciences Mathematics::Geometric Topology Virtual knot Finite sequence Combinatorics Mathematics - Geometric Topology 010201 computation theory & mathematics ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 57M25 FOS: Mathematics Discrete Mathematics and Combinatorics 0101 mathematics Invariant (mathematics) Writhe Mathematics |
| DOI: | 10.48550/arxiv.1905.03489 |
| Popis: | The writhe polynomial is a fundamental invariant of an oriented virtual knot. We introduce a kind of local moves for oriented virtual knots called shell moves. The first aim of this paper is to prove that two oriented virtual knots have the same writhe polynomial if and only if they are related by a finite sequence of shell moves. The second aim of this paper is to classify oriented $2$-component virtual links up to shell moves by using several invariants of virtual links. Comment: 26 pages, 25 figures |
| Databáze: | OpenAIRE |
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