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.
1
City University of New York, USA
2
Rice University, Houston, USA
Daniel Berlyne; Jacob Russell. Hierarchical hyperbolicity of graph products. Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 523-580. doi: 10.4171/ggd/652
@article{10_4171_ggd_652,
author = {Daniel Berlyne and Jacob Russell},
title = {Hierarchical hyperbolicity of graph products},
journal = {Groups, geometry, and dynamics},
pages = {523--580},
year = {2022},
volume = {16},
number = {2},
doi = {10.4171/ggd/652},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/652/}
}
TY - JOUR
AU - Daniel Berlyne
AU - Jacob Russell
TI - Hierarchical hyperbolicity of graph products
JO - Groups, geometry, and dynamics
PY - 2022
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UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/652/
DO - 10.4171/ggd/652
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