ON THE Δ-UNKNOTTING NUMBER OF WHITEHEAD DOUBLES OF KNOTS-Reference-Cited by-同舟云学术

ON THE Δ-UNKNOTTING NUMBER OF WHITEHEAD DOUBLES OF KNOTS

Published:2012-02 Issue:02 Volume:21 Page:1250021
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

JANG HEE JEONG¹,LEE SANG YOUL²,SEO MYOUNGSOO³

Affiliation:

1. Department of Mathematics, Graduate School of Natural Sciences, Pusan National University, Pusan 609-735, Korea

2. Department of Mathematics, Pusan National University, Pusan 609-735, Korea

3. Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea

Abstract

In this paper, we give a bound for the Δ-unknotting number of a Whitehead double in terms of the unknotting number and a certain integral invariant of its companion knot. As applications, we show that the Δ-unknotting number of m-twisted Whitehead doubles of certain knots does not remember its companion knot, and is equal to the twist number m. We also give possible Δ-unknotting number of m-twisted Whitehead doubles whose companions are knots with unknotting number 1, certain twist knots, amphicheiral knots, and positive knots.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216511009583

Reference36 articles.

1. Casson's Invariant for Oriented Homology Three-Spheres

2. ON THE KINKINESS OF CLOSED BRAIDS

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