论文标题
作用于CAT（0）立方体配合物的组均匀指数生长
Groups acting on CAT(0) cube complexes with uniform exponential growth
论文作者
论文摘要
我们研究作用于CAT（0）立方体配合物的组的统一指数生长。我们表明，在CAT（0）平方复合物上没有全局固定点的组的组具有统一的指数生长或稳定欧几里得子复合物。这概括了考虑自由行动的Kar和Sageev的工作。我们的结果使我们能够显示出某些对CAT（0）正方形复合物不适当的群体的统一指数增长，即Higman组和无三角形Artin组的有限生成的亚组。我们还获得了与任何隔离平面的任何尺寸的非虚拟阿贝尔群体，该基团具有孤立的平底鞋，这些平底鞋接受了几何群体的作用具有统一的指数生长。
We study uniform exponential growth of groups acting on CAT(0) cube complexes. We show that groups acting without global fixed points on CAT(0) square complexes either have uniform exponential growth or stabilize a Euclidean subcomplex. This generalizes the work of Kar and Sageev that considers free actions. Our result lets us show uniform exponential growth for certain groups that act improperly on CAT(0) square complexes, namely, finitely generated subgroups of the Higman group and triangle-free Artin groups. We also obtain that non-virtually abelian groups acting freely on CAT(0) cube complexes of any dimension with isolated flats that admit a geometric group action have uniform exponential growth.
