论文标题
弱特殊的正方形复合物的准染色器不变性
Quasi-isometry invariants of weakly special square complexes
论文作者
论文摘要
我们为紧凑型弱特殊的正方形复合物的通用覆盖定义了相交复合物，并表明它是准时的不变性。通过使用这种准静电法不变，我们研究了二维右角ARTIN组和平面图2-编式组的准等级分类。我们的结果涵盖了两个二维右角Artin组的著名案例：（1）那些定义图是树木的案例，以及（2）那些外部自动构成组有限的案例。最后，我们表明，有许多无限的图2编织组是对右角artin组的准均衡，而不是无限的。
We define the intersection complex for the universal cover of a compact weakly special square complex and show that it is a quasi-isometry invariant. By using this quasi-isometry invariant, we study the quasi-isometric classification of 2-dimensional right-angled Artin groups and planar graph 2-braid groups. Our results cover two well-known cases of 2-dimensional right-angled Artin groups: (1) those whose defining graphs are trees and (2) those whose outer automorphism groups are finite. Finally, we show that there are infinitely many graph 2-braid groups which are quasi-isometric to right-angled Artin groups and infinitely many which are not.
