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Full-Text Articles in Physical Sciences and Mathematics
Hierarchical Hyperbolicity Of Graph Products And Graph Braid Groups, Daniel James Solomon Berlyne
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 …
Convexity And Curvature In Hierarchically Hyperbolic Spaces, Jacob Russell-Madonia
Convexity And Curvature In Hierarchically Hyperbolic Spaces, Jacob Russell-Madonia
Dissertations, Theses, and Capstone Projects
Introduced by Behrstock, Hagen, and Sisto, hierarchically hyperbolic spaces axiomatized Masur and Minsky's powerful hierarchy machinery for the mapping class groups. The class of hierarchically hyperbolic spaces encompasses a number of important and seemingly distinct examples in geometric group theory including the mapping class group and Teichmueller space of a surface, virtually compact special groups, and the fundamental groups of 3-manifolds without Nil or Sol components. This generalization allows the geometry of all of these important examples to be studied simultaneously as well as providing a bridge for techniques from one area to be applied to another.
This thesis presents …