Surface group amalgams that (don't) act on 3-manifolds
Surface group amalgams that (don't) act on 3-manifolds
复制标题
（不）作用于 3 流形的表面基团汞齐
DOI：
10.1353/ajm.2020.0020
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
H. Tran
中科院分区：
文献类型：
--
作者：
G. Hruska;Emily Stark;H. Tran
摘要：我们确定了在简单闭曲线的倍数上确定的曲面群的合并积不是$3流形的基本群。我们证明了所考虑的每个曲面汞齐实际上是$3-流形的基本群。我们证明了每个这样的表面群的汞齐都抽象地可公化为来自相关家族的直角Coxeter群。在附录中，我们确定了这些曲面汞齐及其相关直角Coxeter群之间的拟等距类。
Abstract:We determine which amalgamated products of surface groups identified over multiples of simple closed curves are not fundamental groups of $3$-manifolds. We prove each surface amalgam considered is virtually the fundamental group of a $3$-manifold. We prove that each such surface group amalgam is abstractly commensurable to a right-angled Coxeter group from a related family. In an appendix, we determine the quasi-isometry classes among these surface amalgams and their related right-angled Coxeter groups.