(1, 2) and weak (1, 3) homotopies on knot projections

Noboru Ito, Yusuke Takimura

研究成果: Article

13 引用 (Scopus)


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).

ジャーナルJournal of Knot Theory and its Ramifications
出版物ステータスPublished - 2013 12

ASJC Scopus subject areas

  • Algebra and Number Theory

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