(1, 2) AND WEAK (1, 3) HOMOTOPIES ON KNOT PROJECTIONS-Reference-Cited by-同舟云学术

(1, 2) AND WEAK (1, 3) HOMOTOPIES ON KNOT PROJECTIONS

Published:2013-12 Issue:14 Volume:22 Page:1350085
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

ITO NOBORU¹,TAKIMURA YUSUKE²

Affiliation:

1. Waseda Institute for Advanced Study, 1-6-1, Nishi Waseda Shinjuku-ku Tokyo 169-8050, Japan

2. Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

Abstract

In this paper, we obtain the necessary and sufficient condition that two knot projections are related by a finite sequence of the first and second flat Reidemeister moves (Theorem 2.2). We also consider an equivalence relation that is called weak (1, 3) homotopy. This equivalence relation occurs by the first flat Reidemeister move and one of the third flat Reidemeister moves. We introduce a map sending weak (1, 3) homotopy classes to knot isotopy classes (Sec. 3). Using the map, we determine which knot projections are trivialized under weak (1, 3) homotopy (Corollary 4.1).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216513500855

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