论文标题
三弦和强（1，2）同喻
Triple chords and strong (1, 2) homotopy
论文作者
论文摘要
三和弦是一个和弦图的子三图，由一个圆圈组成，有限的许多和弦连接球形曲线上每个双点的预图像，并且它具有三个和弦，提供了三个和弦。本文描述了三和弦的数量与称为强（1，2）同型的等价关系之间的一些关系，该关系由第一种和一种涉及逆向自距离的第二种和第二种reidemister moves组成，如果曲线具有任何方向。我们表明，如果是简单的闭合曲线或一个没有1个和2 gon的素声的质曲线或素打突出，则素的打击被强（1，2）同质副本进行了微不足道，其和弦图不包含任何三弦。我们还讨论了Shimizu的还原性与三弦之间的关系。
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, and it has exactly three chords giving the triple intersection. 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 prime 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.
