Isometries of CAT(0) cube complexes are semi-simple
Isometries of CAT(0) cube complexes are semi-simple
复制标题
CAT(0) 立方体复合体的等轴测图是半简单的
DOI：
10.1007/s40316-021-00186-2
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Frédéric Haglund
中科院分区：
文献类型：
--
作者：
Frédéric Haglund
我们考虑任意cat(0)立方复合体的自同构。我们研究了它的组合位移，证明了自同构要么有一个不动点，要么保留了某个组合轴。因此，当一个fg群包含一个扭曲的循环子群时，它在有壁的离散空间上不允许有适当的作用。作为应用，Baumslag-Solitar群和Heisenberg群提供了群在有墙的测量空间上有适当作用，但在有墙的离散空间上没有适当作用的例子。
We consider an automorphism of an arbitraryCAT(0) cube complex. We study its combinatorial displacement and we show that either the automorphism has a fixed point or it preserves some combinatorial axis. It follows that when a f.g. group contains a distorted cyclic subgroup, it admits no proper action on a discrete space with walls. As an application Baumslag-Solitar groups and Heisenberg groups provide examples of groups having a proper action on measured spaces with walls, but no proper action on a discrete space with wall.