论文标题
图形产品的分层双曲线
Hierarchical hyperbolicity of graph products
论文作者
论文摘要
我们表明，相对于其顶点组，有限生成的组的任何图形均为分层双曲线。我们将此结果应用于回答Behrstock，Hagen和Sisto的两个问题：我们表明，任何图形产品上的音节度量构成层次上的双曲线空间，并且层次上双曲线组的图形本身就是分层双曲线群。最后的结果是通过消除对顶点组上额外的假设的需要来加强贝莱和罗比奥的结果。我们还回答了有关有限基团的图形产物电气化的几何形状的两个问题。
We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this result to answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on any graph product forms a hierarchically hyperbolic space, and that graph products of hierarchically hyperbolic groups are themselves hierarchically hyperbolic groups. This last result is a strengthening of a result of Berlai and Robbio by removing the need for extra hypotheses on the vertex groups. We also answer two questions of Genevois about the geometry of the electrification of a graph product of finite groups.
