RIBBON 2-KNOTS WITH DISTINCT RIBBON TYPES
RIBBON 2-KNOTS WITH DISTINCT RIBBON TYPES
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具有不同织带类型的 2 结织带
DOI：
10.1142/s0218216509007579
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发表时间：
2009
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
带状2结是R4中的2球，由R4中的m个2球与m - 1管连接而成。即使在带状2结K2是由两个2球和一根管子构成的情况下，构造K2的方法也并不总是唯一的。也就是说，K2可能有两种或两种以上的表现形式。一根管子穿过两个球体n次的表示被称为n交叉带表示，n也是这个表示的带交叉数。在本文中，我们将证明，对于任意正整数i，存在两种不同类型的带状2结，其带状交叉数之差为i；另外，我们还会证明，对于任意正整数j，存在一个带2结，有j的表示形式，不同的类型使得它们有相同的带交叉数。
A ribbon 2-knot is a 2-sphere in R4, which is obtained from m 2-spheres in R4 by connecting them with m - 1 pipes. Even in the case that a ribbon 2-knot K2 is constructed by two 2-spheres and one pipe, a way of constructing K2 is not always unique. That is, K2 might have presentations of two or more types. The presentation that a pipe crosses two spheres n times is said to be an n-crossing ribbon presentation, and also n be the ribbon crossing number of this presentation. In this note, we will show that for any positive integer i, there exists a ribbon 2-knot with presentations of two distinct types such that the difference of their ribbon crossing number is i; and in addition we will also show that for any positive integer j, there exists a ribbon 2-knot with presentations of j, distinct types such that they have the same ribbon crossing number.