论文标题
分区表面的Torelli组的拓扑和动力学特性
Topological and dynamical properties of Torelli groups of partitioned surfaces
论文作者
论文摘要
普特曼（Putman）引入了一个分区表面的概念，该表面是一个具有边界的表面，限制了表面如何嵌入较大的表面，并定义了分区表面的Torelli组。在本文中，我们研究了分区表面的Torelli组的一些拓扑和动力学方面。更准确地说，首先，我们在分区表面的Torelli组的共同体学维度上获得上和下限，并表明当最多三个边界组件组合在一起时，这两个边界是重合的。其次，我们研究了相应曲线复合物上分隔表面的摩尔利群体组的渐近翻译长度。我们表明，最小的渐近翻译长度在渐近上的行为几乎就像表面的欧拉特征的倒数一样。这概括了Torelli组的第一和第二作者的先前结果。
Putman introduced a notion of a partitioned surface which is a surface with boundary with decoration restricting how the surface can be embedded into larger surfaces, and defined the Torelli group of the partitioned surfaces. In this paper, we study some topological and dynamical aspects of the Torelli groups of partitioned surfaces. More precisely, first we obtain upper and lower bounds on the cohomological dimension of Torelli groups of partitioned surfaces and show that those two bounds coincide when at most three boundary components are grouped together in the partition of the boundary. Second, we study the asymptotic translation lengths of Torelli groups of partitioned surfaces on the corresponding curve complexes. We show that the minimal asymptotic translation length asymptotically behaves almost like the reciprocal of the Euler characteristic of the surface. This generalizes the previous result of the first and second authors on Torelli groups for closed surfaces.
