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arXiv · 2006.03085

Hierarchical hyperbolicity of graph products

Daniel Berlyne·Jacob Russell
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Abstract

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.

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Daniel Berlyne, Jacob Russell. 2020-06-04. Hierarchical hyperbolicity of graph products. https://arxiv.org/abs/2006.03085

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