A classification of (1, 1) -positions

Bo Hyun Kwon; Jung Hoon Lee

doi:10.1142/S0218216520500509

A classification of (1, 1) -positions

Bo Hyun Kwon
, Jung Hoon Lee

Department of Mathematics

Korea University

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

Abstract

In this paper, we describe the equivalence classes of simple arcs between the two punctures on a 2-punctured torus ς1,2 up to isotopy by using the given four generators g1,g2,g3 and g4. Actually, we show that a class of simple arcs is represented by an ordered sequence of four integers. Also, we introduce an algorithm to check whether or not an ordered sequence of four integers represents a class of simple arcs in ς1,2. We want to point out that this result classifies the (1, 1)-positions.

Original language	English
Article number	2050050
Journal	Journal of Knot Theory and its Ramifications
Volume	29
Issue number	7
DOIs	https://doi.org/10.1142/S0218216520500509
State	Published - 2020.06.1

Keywords

(1,1)-Position
Dehn's theorem
train track

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1142/S0218216520500509

Cite this

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title = "A classification of (1, 1) -positions",

abstract = "In this paper, we describe the equivalence classes of simple arcs between the two punctures on a 2-punctured torus ς1,2 up to isotopy by using the given four generators g1,g2,g3 and g4. Actually, we show that a class of simple arcs is represented by an ordered sequence of four integers. Also, we introduce an algorithm to check whether or not an ordered sequence of four integers represents a class of simple arcs in ς1,2. We want to point out that this result classifies the (1, 1)-positions.",

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AU - Lee, Jung Hoon

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AB - In this paper, we describe the equivalence classes of simple arcs between the two punctures on a 2-punctured torus ς1,2 up to isotopy by using the given four generators g1,g2,g3 and g4. Actually, we show that a class of simple arcs is represented by an ordered sequence of four integers. Also, we introduce an algorithm to check whether or not an ordered sequence of four integers represents a class of simple arcs in ς1,2. We want to point out that this result classifies the (1, 1)-positions.

KW - (1,1)-Position

KW - Dehn's theorem

KW - train track

UR - https://www.scopus.com/pages/publications/85090844973

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DO - 10.1142/S0218216520500509

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AN - SCOPUS:85090844973

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JO - Journal of Knot Theory and its Ramifications

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IS - 7

M1 - 2050050

ER -

A classification of (1, 1) -positions

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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