论文标题
Haken定理的独特性
Uniqueness in Haken's Theorem
论文作者
论文摘要
在Haken和Casson-Gordon之后，它在[SC]中显示了在Heegaard拆分歧管M中减少球体或减少边界的磁盘E，可以将Heegaard表面T t同位素进行同位素，使其在一个圆圈中相交E。在这里我们表明，当t的两个不同位置实现这一点时，一个可以通过一系列序列移动到另一个 1）t rel e的同位素 2）推动一对稳定的T通过E和 3）t的眼曲。 最后一举一动的灵感来自鲍威尔为Goeritz集团提议的发电机之一。
Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk E in a Heegaard split manifold M, the Heegaard surface T can be isotoped so that it intersects E in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel E 2) pushing a stabilizing pair of T through E and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group.
