RIBBON TORUS KNOTS PRESENTED BY VIRTUAL KNOTS WITH UP TO FOUR CROSSINGS-Reference-Cited by-同舟云学术

RIBBON TORUS KNOTS PRESENTED BY VIRTUAL KNOTS WITH UP TO FOUR CROSSINGS

Published:2012-10-24 Issue:13 Volume:21 Page:1240005
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

ICHIMORI ATSUSHI¹,KANENOBU TAIZO¹

Affiliation:

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

Abstract

A ribbon torus knot embedded in the 4-space is presented by a welded virtual knot through the tube operation due to Shin Satoh. We make an attempt of classification of ribbon torus knots presented by virtual knots with up to four crossings, where we use the list of virtual knots enumerated by Jeremy Green. We mainly investigate the groups of virtual knots.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216512400056

Reference27 articles.

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3. R. H. Fox, Topology of 3-Manifolds and Related Topics (Prentice-Hall, 1962) pp. 120–167.

4. Finite-type invariants of classical and virtual knots

5. Abelian normal subgroups of two-knot groups

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