Hierarchical hyperbolicity of graph products
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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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Berlyne, Daniel and Russell, Jacob. "Hierarchical hyperbolicity of graph products." Groups, Geometry, and Dynamics, 16, no. 2 (2022) EMS Press: 523-580. https://doi.org/10.4171/ggd/652.