AN UNKNOTTING OPERATION ON RIBBON 2-KNOTS-Reference-Cited by-同舟云学术

AN UNKNOTTING OPERATION ON RIBBON 2-KNOTS

Published:2000-12 Issue:08 Volume:09 Page:1011-1028
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

KANENOBU TAIZO¹

Affiliation:

1. Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Abstract

We define a local move on a ribbon 2-knot diagram, called an HC-move. We show that it is an unknotting operation for a ribbon 2-knot, and that the application of a single HC-move to a ribbon 2-knot changes the second derivative at t=1 of its normalized Alexander polynomial by either ±2 or 0. This result is applied to the calculation of the HC-unknotting numbers of ribbon 2-knots. We also consider a relation with a 1-handle unknotting operation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216500000608

Reference18 articles.

1. FIRST COMMON TERMS OF THE HOMFLY AND KAUFFMAN POLYNOMIALS, AND THE CONWAY POLYNOMIAL OF A KNOT

2. WEAK UNKNOTTING NUMBER OF A COMPOSITE 2-KNOT

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