Quasi-isometries preserve the geometric decomposition of Haken manifolds
Quasi-isometries preserve the geometric decomposition of Haken manifolds
复制标题
拟等距保留哈肯流形的几何分解
DOI：
10.1007/s002220050145
复制
发表时间：
1997
影响因子：
3.1
通讯作者：
B. Leeb
中科院分区：
文献类型：
--
作者：
M. Kapovich;B. Leeb
摘要：我们证明了具有零欧拉特征线的哈肯三维流形的基本群的正则分解的拟等距不变性。证明了具有非平凡标准分解的Haken流形群的拟等距群是Haken轨道群的有限扩张。作为一个副产品，我们描述了所有的2维拟平坦的通用覆盖的非几何哈肯流形。
Abstract.We prove quasi-isometry invariance of the canonical decomposition for fundamental groups of Haken 3-manifolds with zero Euler characteristic. We show that groups quasi-isometric to Haken manifold groups with nontrivial canonical decomposition are finite extensions of Haken orbifold groups. As a by-product we describe all 2-dimensional quasi-flats in the universal covers of non-geometric Haken manifolds.