On the virtual Alexander polynomial of periodic virtual knots-Reference-Cited by-同舟云学术

On the virtual Alexander polynomial of periodic virtual knots

Published:2014-06 Issue:07 Volume:23 Page:1460011
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Kim Joonoh¹,Lee Sang Youl¹,Seo Myoungsoo²

Affiliation:

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

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

Abstract

In this paper, we give a relationship between the virtual Alexander polynomial of a periodic virtual knot and that of its factor knot. As an application, we improve Im–Lee's table of possible periods of 117 virtual knots with classical crossings ≤ 4 in Jeremy Green's table. In particular, we prove that the virtual knots 4.1 and 4.77 have the actual period 2 and no others, and the virtual knot 4.99 has the actual period 2.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216514600116

Reference12 articles.

1. ON THE INDEX AND ARROW POLYNOMIALS OF PERIDOIC VIRTUAL LINKS

2. The Conway Polynomial in R3 and in Thickened Surfaces: A New Determinant Formulation

3. PERIODIC VIRTUAL LINKS AND THE BINARY BRACKET POLYNOMIAL

4. Virtual Knot Theory

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