Unknotting number and number of Reidemeister moves needed for unlinking

Chuichiro Hayashi; Miwa Hayashi; Tahl Nowik

doi:https://doi.org/10.1016/j.topol.2012.01.008

Unknotting number and number of Reidemeister moves needed for unlinking

Chuichiro Hayashi, Miwa Hayashi, Tahl Nowik

Department of Mathematics

Bar-Ilan University

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

Abstract

Using unknotting number, we introduce a link diagram invariant of type given in Hass and Nowik (2008) [4], which changes at most by 2 under a Reidemeister move. We show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being splitted with respect to the number of crossings.

Original language	English
Pages (from-to)	1467-1474
Number of pages	8
Journal	Topology and its Applications
Volume	159
Issue number	5
DOIs	https://doi.org/10.1016/j.topol.2012.01.008
State	Published - 15 Mar 2012

Keywords

Link diagram
Link diagram invariant
Reidemeister move
Unknotting number

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1016/j.topol.2012.01.008

Cite this

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title = "Unknotting number and number of Reidemeister moves needed for unlinking",

abstract = "Using unknotting number, we introduce a link diagram invariant of type given in Hass and Nowik (2008) [4], which changes at most by 2 under a Reidemeister move. We show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being splitted with respect to the number of crossings.",

keywords = "Link diagram, Link diagram invariant, Reidemeister move, Unknotting number",

author = "Chuichiro Hayashi and Miwa Hayashi and Tahl Nowik",

note = "Funding Information: E-mail addresses: [email protected] (C. Hayashi), [email protected] (M. Hayashi), [email protected] (T. Nowik). 1 The author is partially supported by Grant-in-Aid for Scientific Research (No. 22540101), Ministry of Education, Science, Sports and Technology, Japan.",

year = "2012",

month = mar,

day = "15",

doi = "https://doi.org/10.1016/j.topol.2012.01.008",

language = "الإنجليزيّة",

volume = "159",

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journal = "Topology and its Applications",

issn = "0166-8641",

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TY - JOUR

T1 - Unknotting number and number of Reidemeister moves needed for unlinking

AU - Hayashi, Chuichiro

AU - Hayashi, Miwa

AU - Nowik, Tahl

N1 - Funding Information: E-mail addresses: [email protected] (C. Hayashi), [email protected] (M. Hayashi), [email protected] (T. Nowik). 1 The author is partially supported by Grant-in-Aid for Scientific Research (No. 22540101), Ministry of Education, Science, Sports and Technology, Japan.

PY - 2012/3/15

Y1 - 2012/3/15

N2 - Using unknotting number, we introduce a link diagram invariant of type given in Hass and Nowik (2008) [4], which changes at most by 2 under a Reidemeister move. We show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being splitted with respect to the number of crossings.

AB - Using unknotting number, we introduce a link diagram invariant of type given in Hass and Nowik (2008) [4], which changes at most by 2 under a Reidemeister move. We show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being splitted with respect to the number of crossings.

KW - Link diagram

KW - Link diagram invariant

KW - Reidemeister move

KW - Unknotting number

UR - http://www.scopus.com/inward/record.url?scp=84856356425&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.topol.2012.01.008

DO - https://doi.org/10.1016/j.topol.2012.01.008

M3 - مقالة

SN - 0166-8641

VL - 159

SP - 1467

EP - 1474

JO - Topology and its Applications

JF - Topology and its Applications

IS - 5

ER -

Unknotting number and number of Reidemeister moves needed for unlinking

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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