Ribbon 2-knots of ribbon crossing number four
Ribbon 2-knots of ribbon crossing number four
复制标题
丝带 2 结丝带交叉数第四
DOI：
10.1142/s021821651850058x
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发表时间：
2018
影响因子：
0.5
通讯作者：
T. Yasuda
中科院分区：
文献类型：
--
作者：
T. Yasuda
A [公式：see text]-knot是[Formula：see text]中与[Formula：see text]同胚的曲面，即[Formula：see text]-空间中的标准球面。丝带[公式：see text]-knot是从[Formula：see text] [Formula：see text]中的[Formula：see text]-sphere通过[Formula：see text]管道连接它们而获得的[Formula：see text]-knot。设[Formula：see text]为丝带2结。由[Formula：see text]-[Formula：see text]表示的带状交叉数是带状线[Formula：see text]-结[Formula：see text]的数值不变量。在[T. Yasuda，Crossing and base numbers of ribbon 2-knots，J. Knot Theory Ramifications 10（2001）999-1003]我们证明了只存在[Formula：see text] ribbon [Formula：see text]-knots of ribbon crossing number up to three.在本文中，我们表明，存在不超过[公式：见文字]带状[公式：见文字]-结的带状交叉数4。
A [Formula: see text]-knot is a surface in [Formula: see text] that is homeomorphic to [Formula: see text], the standard sphere in [Formula: see text]-space. A ribbon [Formula: see text]-knot is a [Formula: see text]-knot obtained from [Formula: see text] [Formula: see text]-spheres in [Formula: see text] by connecting them with [Formula: see text] pipes. Let [Formula: see text] be a ribbon 2-knot. The ribbon crossing number, denoted by [Formula: see text]-[Formula: see text], is a numerical invariant of the ribbon [Formula: see text]-knot [Formula: see text]. In [T. Yasuda, Crossing and base numbers of ribbon 2-knots, J. Knot Theory Ramifications 10 (2001) 999–1003] we showed that there exist just [Formula: see text] ribbon [Formula: see text]-knots of the ribbon crossing number up to three. In this paper, we show that there exist no more than [Formula: see text] ribbon [Formula: see text]-knots of ribbon crossing number four.