On Gauss diagrams of periodic virtual knots

Yongju Bae; In Sook Lee

doi:10.1142/S0218216515400088

On Gauss diagrams of periodic virtual knots

Yongju Bae, In Sook Lee

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

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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).

Original language	English
Article number	1540008
Journal	Journal of Knot Theory and its Ramifications
Volume	24
Issue number	10
DOIs	https://doi.org/10.1142/S0218216515400088
State	Published - 2 Sep 2015

Keywords

affine index polynomial
covering graph
Gauss diagram
periodic Gauss diagram
periodic virtual knot
writhe polynomial

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10.1142/S0218216515400088

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AB - 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).

KW - affine index polynomial

KW - covering graph

KW - Gauss diagram

KW - periodic Gauss diagram

KW - periodic virtual knot

KW - writhe polynomial

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On Gauss diagrams of periodic virtual knots

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Keywords

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