On groups with Schottky set boundary
Peter Ha\"issinsky, Luisa Paoluzzi, and Genevieve Walsh
TL;DR
This paper investigates relatively hyperbolic groups with boundaries that are Schottky sets, providing characterizations based on the incidence graph components of these sets.
Contribution
It offers a new characterization of such groups by analyzing the incidence graphs of their Schottky set boundaries.
Findings
Characterized groups with boundaries having Schottky sets with 1 or 2 incidence graph components.
Provided criteria linking boundary structure to group properties.
Abstract
We study relatively hyperbolic group pairs whose boundaries are Schottky sets. We characterize the groups that have boundaries where the Schottky sets have incidence graphs with 1 or 2 components.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · semigroups and automata theory