A classification of (1,1)-positions
- Authors
- Kwon, Bo-Hyun; Lee, Jung Hoon
- Issue Date
- 6월-2020
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- (1,1)-Position; Dehn' s theorem; train track
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.29, no.7
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 29
- Number
- 7
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/55442
- DOI
- 10.1142/S0218216520500509
- ISSN
- 0218-2165
- Abstract
- In this paper, we describe the equivalence classes of simple arcs between the two punctures on a 2-punctured torus Sigma(1,2) up to isotopy by using the given four generators g(1), g(2), g(3) and g(4). 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 Sigma(1,2). We want to point out that this result classifies the (1, 1)-positions.
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