Normal forms for rational 3-tangles

Bo hyun Kwon; Jung Hoon Lee

doi:10.1016/j.topol.2025.109388

Normal forms for rational 3-tangles

Bo hyun Kwon^*
, Jung Hoon Lee

^*Corresponding author for this work

Department of Mathematics

Ulsan National Institute of Science and Technology

Research output: Contribution to journal › Journal article › peer-review

Abstract

A collection of properly embedded three disjoint simple arcs in Σ_0,6 represents a rational 3-tangle. In this paper, we define a normal form of collections of three disjoint bridge arcs for a given rational 3-tangle. We show that there is a sequence of operations called normal jump moves which makes a path between arbitrary two elements in the set of normal forms of the same rational 3-tangle. We believe that the normal form would give a clue to classify rational 3-tangles.

Original language	English
Article number	109388
Journal	Topology and its Applications
Volume	369
DOIs	https://doi.org/10.1016/j.topol.2025.109388
State	Published - 2025.08.1

Keywords

Bridge arc replacement
Normal form
Normal jump move
Rational 3-tangle

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.topol.2025.109388

Cite this

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title = "Normal forms for rational 3-tangles",

abstract = "A collection of properly embedded three disjoint simple arcs in Σ0,6 represents a rational 3-tangle. In this paper, we define a normal form of collections of three disjoint bridge arcs for a given rational 3-tangle. We show that there is a sequence of operations called normal jump moves which makes a path between arbitrary two elements in the set of normal forms of the same rational 3-tangle. We believe that the normal form would give a clue to classify rational 3-tangles.",

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AU - Kwon, Bo hyun

AU - Lee, Jung Hoon

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N2 - A collection of properly embedded three disjoint simple arcs in Σ0,6 represents a rational 3-tangle. In this paper, we define a normal form of collections of three disjoint bridge arcs for a given rational 3-tangle. We show that there is a sequence of operations called normal jump moves which makes a path between arbitrary two elements in the set of normal forms of the same rational 3-tangle. We believe that the normal form would give a clue to classify rational 3-tangles.

AB - A collection of properly embedded three disjoint simple arcs in Σ0,6 represents a rational 3-tangle. In this paper, we define a normal form of collections of three disjoint bridge arcs for a given rational 3-tangle. We show that there is a sequence of operations called normal jump moves which makes a path between arbitrary two elements in the set of normal forms of the same rational 3-tangle. We believe that the normal form would give a clue to classify rational 3-tangles.

KW - Bridge arc replacement

KW - Normal form

KW - Normal jump move

KW - Rational 3-tangle

UR - https://www.scopus.com/pages/publications/105002410963

U2 - 10.1016/j.topol.2025.109388

DO - 10.1016/j.topol.2025.109388

M3 - Journal article

AN - SCOPUS:105002410963

SN - 0166-8641

VL - 369

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 109388

ER -

Normal forms for rational 3-tangles

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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