论文标题
群的图形复合物
Graphical complexes of groups
论文作者
论文摘要
我们介绍了组的图形复合物，可以将其视为具有一维神经的Coxeter系统的概括。我们表明这些络合物是严格开发的，我们为所得的基本结构配备了三个非阳性曲率结构：分段线性猫（0），C（6）图形小取消和收缩期。然后，我们使用这些结构来建立这些复合物的基本组的各种特性，例如双重性和山雀替代品。我们隔离一个易于检查的条件，意味着基本组的双曲线，并构建了一些非纤维化示例。我们还简要讨论了C（4）-t（4）组的图形复合物的平行理论，并概述了它们的基本属性。
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with three structures of non-positive curvature: piecewise linear CAT(0), C(6) graphical small cancellation, and a systolic one. We then use these structures to establish various properties of the fundamental groups of these complexes, such as biautomaticity and Tits Alternative. We isolate an easily checkable condition implying hyperbolicity of the fundamental groups, and we construct some non-hyperbolic examples. We also briefly discuss a parallel theory of C(4)-T(4) graphical complexes of groups and outline their basic properties.
