Satellite constructions and geometric classification of Brunnian links
Satellite constructions and geometric classification of Brunnian links
复制标题
布伦尼亚链路的卫星构造和几何分类
DOI：
10.1142/s0218216521400058
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发表时间：
2021-09-01
影响因子：
0.5
通讯作者：
Ma，Jiming
中科院分区：
文献类型：
--
作者：
Bai，Sheng;Ma，Jiming
我们研究布伦尼亚链路上的卫星运行。首先，我们发现两个特殊的卫星操作，两者都可以从几乎每个布伦尼亚链路构建无限多个不同的布伦尼亚链路。其次，我们给出了Brunnian链接的几何分类定理，描述了Budney在[JSJ-[公式：见正文]中的结和链接补语的分解，Enseign中定义的陪伴图。数学。 3 (2005) 319–359]，并为 Brunnian 链接开发了一种比 JSJ 分解更简单的规范几何分解。 Brunnian 链接的构建块是 Hopf [公式：参见文本]-链接、双曲 Brunnian 链接以及 unlink-complements 中的双曲 Brunnian 链接。第三，我们在[公式：见正文]中定义了一个将unlink-complement中的Brunnian链接减少为新的Brunnian链接的操作，并指出了与该操作有关的一些现象。
We study satellite operations on Brunnian links. First, we find two special satellite operations, both of which can construct infinitely many distinct Brunnian links from almost every Brunnian link. Second, we give a geometric classification theorem for Brunnian links, characterize the companionship graph defined by Budney in [JSJ-decompositions of knot and link complements in [Formula: see text], Enseign. Math. 3 (2005) 319–359], and develop a canonical geometric decomposition, which is simpler than JSJ-decomposition, for Brunnian links. The building blocks of Brunnian links then turn out to be Hopf [Formula: see text]-links, hyperbolic Brunnian links, and hyperbolic Brunnian links in unlink-complements. Third, we define an operation to reduce a Brunnian link in an unlink-complement into a new Brunnian link in [Formula: see text] and point out some phenomena concerning this operation.