The geometry of the curve graph of a right-angled Artin group
The geometry of the curve graph of a right-angled Artin group
复制标题
DOI：
10.1142/s021819671450009x
复制
发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
Sang-hyun Kim;T. Koberda
中科院分区：
文献类型：
--
作者：
Sang-hyun Kim;T. Koberda
我们通过直角Artin群在扩张图和曲线图上的作用的几何关系，建立了直角Artin群和映射类群之间的类比。本文的中心结果是每个直角Artin群在其扩张图上非圆柱地作用。从这个结果，我们能够开发一个尼尔森-瑟斯顿分类的直角阿廷组中的元素。我们的类比涵盖了直角Artin群和映射类群的子群的代数，以及扩展图和曲线图的几何。在几何方面，我们建立了Masur和Minsky的有界测地线象定理及其距离公式的一个类比。
We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The central result in this paper is the fact that each right-angled Artin group acts acylindrically on its extension graph. From this result we are able to develop a Nielsen--Thurston classification for elements in the right-angled Artin group. Our analogy spans both the algebra regarding subgroups of right-angled Artin groups and mapping class groups, as well as the geometry of the extension graph and the curve graph. On the geometric side, we establish an analogue of Masur and Minsky's Bounded Geodesic Image Theorem and their distance formula.