Connected primitive disk complexes and genus two Goeritz groups of lens spaces
Connected primitive disk complexes and genus two Goeritz groups of lens spaces
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连接的原始圆盘复合体和属两个 Goeritz 透镜组群
DOI：
10.1093/imrn/rnv399
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发表时间：
2016
影响因子：
1
通讯作者：
Yuya Koda
中科院分区：
文献类型：
--
作者：
Sangbum Cho;Yuya Koda
给定三流形的稳定Heegaard分裂，该分裂的原始磁盘复形是由原始磁盘的顶点张成的分裂中的柄体磁盘复形的子复形。在这项工作中，我们研究了原始盘复合体的结构，为每个透镜空间的属2 heegard分裂。特别地，我们证明了在这种连接的当且仅当条件下，对于透镜空间的属2分裂的复合体，并描述了这些复合体的组合结构。作为应用，我们得到了每一个透镜空间的2属Goeritz群的有限表示，即保持透镜空间2属heegard分裂的取向保持同胚的同位素类群。
Given a stabilized Heegaard splitting of a three-manifold, the primitive disk complex for the splitting is the subcomplex of the disk complex for a handlebody in the splitting spanned by the vertices of the primitive disks. In this work, we study the structure of the primitive disk complex for the genus-2 Heegaard splitting of each lens space. In particular, we show that the complex for the genus-2 splitting for the lens spacewithis connected if and only ifand describe the combinatorial structure of each of those complexes. As an application, we obtain a finite presentation of the genus-2 Goeritz group of each of those lens spaces, the group of isotopy classes of orientation preserving homeomorphisms of the lens space that preserve the genus-2 Heegaard splitting of it.