Physical Sciences and Mathematics Commons^™

Hierarchical Hyperbolicity Of Graph Products And Graph Braid Groups, Daniel James Solomon Berlyne

Dissertations, Theses, and Capstone Projects

This thesis comprises three original contributions by the author concerning hierarchical hyperbolicity, a coarse geometric tool developed by Behrstock, Hagen, and Sisto to provide a common framework for studying aspects of non-positive curvature in a wide variety of groups and spaces.

We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this to answer two questions of Genevois about the electrification of a graph product of finite groups. We also answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on a graph product forms a …