THE DEALTERNATING NUMBER AND THE ALTERNATION NUMBER OF A CLOSED 3-BRAID-Reference-Cited by-同舟云学术

THE DEALTERNATING NUMBER AND THE ALTERNATION NUMBER OF A CLOSED 3-BRAID

Published:2010-09 Issue:09 Volume:19 Page:1157-1181
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

ABE TETSUYA¹,KISHIMOTO KENGO¹

Affiliation:

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

Abstract

We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation number) and any braid index.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216510008352

Reference29 articles.

1. AN ESTIMATION OF THE ALTERNATION NUMBER OF A TORUS KNOT

2. Almost alternating links

3. Khovanov Homology: Torsion and Thickness

4. Studying links via closed braids. III. Classifying links which are closed 3-braids

5. Graphs on surfaces and Khovanov homology

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