Haken定理中的唯一性
Uniqueness in Haken's Theorem
AI总结：
本文研究Heegaard曲面在相交于单个圆时的定位唯一性，证明两种不同定位可通过同痕、推过稳定对及眼镜扭转序列相互转换。
摘要：
继Haken和Casson-Gordon之后，[Sc]中证明了：给定Heegaard分裂流形M中的约化球或边界约化圆盘E，Heegaard曲面T可被同痕移动，使其与E相交于单个圆。本文证明：当此结果由T的两种不同定位实现时，可通过以下序列将一种定位移动至另一种：1) T相对于E的同痕；2) 将T的稳定对推过E；3) T的眼镜扭转。最后一种移动受Powell提出的Goeritz群生成元之一启发。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
