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Classification of ribbon 2-knots presented by virtual arcs with up to four crossings

Taizo Kanenobu

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

E-mail Address: kanenobu@sci.osaka-cu.ac.jp

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and

Toshio Sumi

Faculty of Arts and Science, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan

E-mail Address: sumi@artsci.kyushu-u.ac.jp

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https://doi.org/10.1142/S0218216519500676Cited by:2 (Source: Crossref)

Abstract

We consider classification of the oriented ribbon 2-knots presented by virtual arcs with up to four crossings. We show the difference by the 2-fold branched covering space, the Alexander polynomial, the number of representations of the knot group to SL $(2, 𝔽)$ , $𝔽$ a finite field, and the twisted Alexander polynomial.

Keywords:

AMSC: 57Q45, 57M25

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