Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Triple chords and strong (1, 2) homotopy
Noboru ItoYusuke Takimura
Author information
JOURNAL FREE ACCESS

2016 Volume 68 Issue 2 Pages 637-651

Details
Abstract

A triple chord is a sub-diagram of a chord diagram that consists of a circle and finitely many chords connecting the preimages for every double point on a spherical curve. This paper describes some relationships between the number of triple chords and an equivalence relation called strong (1, 2) homotopy, which consists of the first and one kind of the second Reidemeister moves involving inverse self-tangency if the curve is given any orientation. We show that a knot projection is trivialized by strong (1, 2) homotopy, if it is a simple closed curve or a prime knot projection without 1- and 2-gons whose chord diagram does not contain any triple chords. We also discuss the relation between Shimizu's reductivity and triple chords.

Content from these authors

This article cannot obtain the latest cited-by information.

© 2016 The Mathematical Society of Japan
Previous article Next article
feedback
Top