The disk complex and 2-bridge knots

Sangbum Cho; Yuya Koda

doi:10.1142/S021821651850027X

The disk complex and 2-bridge knots

Sangbum Cho, Yuya Koda

Research output: Contribution to journal › Article › peer-review

Abstract

We give a purely combinatorial proof of a result of Kobayashi and Saeki that every genus one 1-bridge position of a nontrivial 2-bridge knot is a stabilization.

Original language	English
Article number	1850027
Journal	Journal of Knot Theory and its Ramifications
Volume	27
Issue number	4
DOIs	https://doi.org/10.1142/S021821651850027X
Publication status	Published - 2018 Apr 1
Externally published	Yes

Keywords

(1, 1)-position
2-bridge knot
2-bridge position
Primitive disk complex

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S021821651850027X

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title = "The disk complex and 2-bridge knots",

abstract = "We give a purely combinatorial proof of a result of Kobayashi and Saeki that every genus one 1-bridge position of a nontrivial 2-bridge knot is a stabilization.",

keywords = "(1, 1)-position, 2-bridge knot, 2-bridge position, Primitive disk complex",

author = "Sangbum Cho and Yuya Koda",

note = "Funding Information: the National Research Foundation of Korea (NRF-2015R1A1A1A05001071) funded by the Ministry of Science, ICT and Future Planning. The second-named author is supported in part by JSPS KAKENHI Grant Numbers 15H03620, 17K05254, 17H06463. Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",

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AU - Koda, Yuya

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N2 - We give a purely combinatorial proof of a result of Kobayashi and Saeki that every genus one 1-bridge position of a nontrivial 2-bridge knot is a stabilization.

AB - We give a purely combinatorial proof of a result of Kobayashi and Saeki that every genus one 1-bridge position of a nontrivial 2-bridge knot is a stabilization.

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KW - 2-bridge knot

KW - 2-bridge position

KW - Primitive disk complex

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The disk complex and 2-bridge knots

Abstract

Keywords

ASJC Scopus subject areas

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