3 papers
math.GR2023
Relative hyperbolicity, thickness, and the hierarchically hyperbolic boundary
Carolyn Abbott, Jason Behrstock, Jacob Russell
We study the boundaries of relatively hyperbolic HHGs. Using the simplicial structure on the hierarchically hyperbolic boundary, we characterize both relative hyperbolicity and bei…
math.GT2023
Largest hyperbolic actions of 3--manifold groups
Carolyn Abbott, Hoang Thanh Nguyen, Alexander J. Rasmussen
The set of equivalence classes of cobounded actions of a group G on different hyperbolic metric spaces carries a natural partial order. Following Abbott--Balasubramanya--Osin, the…
math.GR2022
Valuations, completions, and hyperbolic actions of metabelian groups
Carolyn R. Abbott, Sahana Balasubramanya, Sam Payne +1
Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In thi…