Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions
Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions
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与 Heegaard 分裂和桥分解相关的映射类组的子组
DOI：
10.1007/s10711-015-0094-4
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发表时间：
2016
影响因子：
0.5
通讯作者：
Makoto Sakuma
中科院分区：
文献类型：
--
作者：
Ken'ichi Ohshika;Makoto Sakuma
设为封闭可定向 3-流形 M 的 Heegaard 分裂（或连杆外部的桥分解）。考虑由恒等同伦的保向自同胚表示的映射类组成的映射类群的子群，并设 为作为 的图像获得的曲线复形的自同构群的子群。然后群生成并作用于包含在 M 中同伦类中的每个轨道。在本文中，我们研究了群 G 的结构，并检验同伦类是否可以包含多个轨道。我们还表明，当 Heegaard 分裂满足 R 有界组合且具有高 Hempel 距离时，G 在 Sha 的射影叠层空间上的作用是一个非空的不连续域。
Letbe a Heegaard splitting of a closed orientable 3-manifoldM(or a bridge decomposition of a link exterior). Consider the subgroupof the mapping class group ofconsisting of mapping classes represented by orientation-preserving auto-homeomorphisms ofhomotopic to the identity, and letbe the subgroup of the automorphism group of the curve complexobtained as the image of. Then the groupgenerated byandacts onwith each orbit being contained in a homotopy class inM. In this paper, we study the structure of the groupGand examine whether a homotopy class can contain more than one orbit. We also show that the action ofGon the projective lamination space ofShas a non-empty domain of discontinuity when the Heegaard splitting satisfiesR-bounded combinatorics and has high Hempel distance.