A note on coverings of virtual knots

Nakamura, Takuji; Nakanishi, Yasutaka; Satoh, Shin

doi:10.1142/s0218216519710020

Cited by 3 publications

(2 citation statements)

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“…Since the orientation of shells is determined by the sign of the endpoint of γ, we sometimes omit the orientation of γ. The notion of a shell in this paper is slightly different from that of an anklet in [9].…”

Section: Figure 2 Self-and Nonself-chords Of a Gauss Diagrammentioning

confidence: 98%

Writhe polynomials and shell moves for virtual knots and links

Nakamura

Nakanishi

Satoh

2020

European Journal of Combinatorics

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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.

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Section: Figure 2 Self-and Nonself-chords Of a Gauss Diagrammentioning

confidence: 98%

Writhe polynomials and shell moves for virtual knots and links

Nakamura

Nakanishi

Satoh

2020

European Journal of Combinatorics

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“…We remark that the idea of n -covering was first proposed by Turaev [46]. Recently, a characterization of the n -covering of virtual knots was given by T. Nakamura, Y. Nakanishi, and S. Satoh [39].…”

Section: Introductionmentioning

confidence: 99%

The Chord Index, its Definitions, Applications, and Generalizations

Cheng

2020

Can. J. Math.-J. Can. Math.

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In this paper we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to define finite type invariants of virtual knots. The notions of indexed Jones polynomial and indexed quandle are introduced, which generalize the classical Jones polynomial and knot quandle respectively. Some applications of these new invariants are discussed. We also study how to define a generalized chord index via a fixed finite biquandle. Finally the chord index and its applications in twisted knot theory are discussed.1991 Mathematics Subject Classification. 57M25, 57M27.

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On invariants of multiplexed virtual links

Wada

2024

Int. J. Math.

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For a virtual knot [Formula: see text] and an integer [Formula: see text] with [Formula: see text], we introduce a method of constructing an [Formula: see text]-component virtual link [Formula: see text], which we call the [Formula: see text]-multiplexing of [Formula: see text]. Every invariant of [Formula: see text] is an invariant of [Formula: see text]. We give a way of calculating three kinds of invariants of [Formula: see text] using invariants of [Formula: see text]. As an application of our method, we also show that Manturov’s virtual [Formula: see text]-colorings for [Formula: see text] can be interpreted as certain classical [Formula: see text]-colorings for [Formula: see text].

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A note on coverings of virtual knots

Cited by 3 publications

References 13 publications

Writhe polynomials and shell moves for virtual knots and links

Writhe polynomials and shell moves for virtual knots and links

The Chord Index, its Definitions, Applications, and Generalizations

On invariants of multiplexed virtual links

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