Special issue: 2014 KOOK-TAPU Workshop on Knot Theory and Related TopicsNo Access

On Gauss diagrams of periodic virtual knots

Yongju Bae

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

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and

In Sook Lee

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

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https://doi.org/10.1142/S0218216515400088Cited by:1 (Source: Crossref)

Abstract

In this paper, we study the Gauss diagrams for periodic virtual knots (Theorem 3.1) and show that the virtual knot corresponding to a periodic Gauss diagram is equivalent to the periodic virtual knot whose factor is the virtual knot corresponding to the factor Gauss diagram (Theorem 3.2). We give formulae for the writhe polynomial and the affine index polynomial of periodic virtual knots by using those of factor knots (Corollary 4.2, Corollary 4.6).

Keywords:

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