Special Issue: 2013 TAPU Workshop on Knot Theory and Related TopicsNo Access

On the virtual Alexander polynomial of periodic virtual knots

Joonoh Kim

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

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Sang Youl Lee

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

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, and

Myoungsoo Seo

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

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https://doi.org/10.1142/S0218216514600116Cited by:3 (Source: Crossref)

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.

Keywords:

AMSC: 57M25, 57M27

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