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ON 2-ADJACENCY RELATION OF TWO-BRIDGE KNOTS AND LINKS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  01 February 2008

ICHIRO TORISU
ICHIRO TORISU*
Affiliation:
Naruto University of Education, 748, Nakajima, Takashima, Naruto-cho, Naruto-shi, 772-8502, Japan (email: torisu@naruto-u.ac.jp)
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Abstract

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We give a necessary condition for a two-bridge knot or link S(p,q) to be 2-adjacent to another two-bridge knot or link S(r,s). In particular, we show that if the trivial knot or link is 2-adjacent to S(p,q), then S(p,q) is trivial, that if S(p,q) is 2-adjacent to its mirror image, then S(p,q) is amphicheiral, and that for a prime integer p, if S(p,q) is 2-adjacent to S(r,s), then S(p,q)=S(r,s) or S(r,s)=S(1,0).

Keywords

n-adjacenttwo-bridge knotlinkDehn surgery

MSC classification

Secondary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 1 , February 2008 , pp. 139 - 144
Copyright
Copyright © 2008 Australian Mathematical Society

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