Hierarchical hyperbolicity of graph products

  • Daniel Berlyne

    City University of New York, USA
  • Jacob Russell

    Rice University, Houston, USA
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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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Daniel Berlyne, Jacob Russell, Hierarchical hyperbolicity of graph products. Groups Geom. Dyn. 16 (2022), no. 2, pp. 523–580

DOI 10.4171/GGD/652