On gauss codes of virtual doodles

Bartholomew, Andrew; Fenn, Roger; Kamada, Naoko; Kamada, Seiichi

doi:10.1142/s0218216518430137

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Figure 6 Flat Kishino Knot As Virtual Doodle1

Introduction1

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2020

2024

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Cited by 7 publications

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“…The moves R 1 and R 2 are referred as flat versions of Reidemeister moves for classical knots [6]. An oriented virtual doodle diagram is a doodle diagram with an orientation on each component of the underlying immersion.…”

Section: Figure 6 Flat Kishino Knot As Virtual Doodlementioning

confidence: 99%

Alexander and Markov theorems for virtual doodles

Nanda,

Singh

2020

Preprint

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Study of isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces can be thought of as a planar analogue of virtual knot theory where the genus zero case corresponds to classical knot theory. Alexander and Markov theorems for the genus zero case are known where the role of groups is played by twin groups, a class of right angled Coxeter groups with only far commutativity relations. The purpose of this paper is to prove Alexander and Markov theorems for higher genus case where the role of groups is played by a new class of groups called virtual twin groups which contain twin groups in a natural way.

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Section: Figure 6 Flat Kishino Knot As Virtual Doodlementioning

confidence: 99%

Alexander and Markov theorems for virtual doodles

Nanda,

Singh

2020

Preprint

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“…For instance, every class of a doodle has a unique diagram with minimal number of crossings [19]; the calculation of Vassiliev invariants is more complicated than classical knots, but Vassiliev invariants classify doodles, problem that remains open for knots [23]. Recently, Bartholomew-Fenn-Kamada-Kamada [4] extended the study of doodles to immersed circles on closed oriented surfaces of any genus, which can be considered as virtual links analogue for doodles; in [5] they give a complete invariant for virtual doodles 1 .…”

Section: Introductionmentioning

confidence: 99%