Surface Houghton groups
Surface Houghton groups
复制标题
表面霍顿组
DOI：
10.1007/s00208-023-02751-2
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发表时间：
2023
影响因子：
1.4
通讯作者：
Leininger, Christopher J.
中科院分区：
文献类型：
--
作者：
Aramayona, Javier;Bux, Kai-Uwe;Kim, Heejoung;Leininger, Christopher J.
对于每一个，表面霍顿群被定义为具有精确端点的表面的渐近刚性映射类群，所有端点都是非平面的。这些群类似于并且实际上包含辫状霍顿群。这些群也在拓扑中自然出现：闭合 3 流形的深度 1 叶状结构的纤维成分的每个单向同胚都共轭为 some。作为无限类型表面的可数映射类组，这些组介于经典映射类组和大映射类组之间。我们开始对表面霍顿群进行研究，证明它是类型，但不是类型，类似于辫状霍顿群。
For every, thesurface Houghton groupis defined as the asymptotically rigid mapping class group of a surface with exactlynends, all of them non-planar. The groupsare analogous to, and in fact contain, the braided Houghton groups. These groups also arise naturally in topology: every monodromy homeomorphism of a fibered component of a depth-1 foliation of closed 3-manifold is conjugate into some. As countable mapping class groups of infinite type surfaces, the groupslie somewhere between classical mapping class groups and big mapping class groups. We initiate the study of surface Houghton groups proving, among other things, thatis of type, but not of type, analogous to the braided Houghton groups.