Kleinian groups and the complex of curves
Kleinian groups and the complex of curves
复制标题
克莱尼群和曲线复形
DOI：
--
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Y. Minsky
中科院分区：
文献类型：
--
作者：
Y. Minsky
利用曲面上曲线复合体的组合结构，研究了Kleinian曲面群的内部几何及其与端点渐近几何的关系。我们的主要结果给出了Kleinian群具有“有界几何”（注入半径下界）的必要条件，这是通过使用群的结束不变量和曲线复合体计算的系数序列（地下投影）来表示的。这些结果与在点环表面群中得到的结果直接相似。在这种情况下，结束不变量是闭合单位圆盘上的点，其系数与经典的连续分数系数密切相关。在这种情况下，所得到的估计对Thurston的末层猜想的解起着至关重要的作用。
We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our main results give necessary conditions for the Kleinian group to have ‘bounded geometry’ (lower bounds on injectivity radius) in terms of a sequence of coecients (subsurface projections) computed using the ending invariants of the group and the complex of curves. These results are directly analogous to those obtained in the case of puncturedtorus surface groups. In that setting the ending invariants are points in the closed unit disk and the coecients are closely related to classical continuedfraction coecients. The estimates obtained play an essential role in the solution of Thurston’s ending lamination conjecture in that case.