TL;DR
This paper reviews the theory of Cannon-Thurston maps, highlighting their role in connecting complex analysis and hyperbolic geometry in the study of Kleinian groups, and discusses related open questions.
Contribution
It provides an overview of Cannon-Thurston maps and explores their connections to hyperbolic subgroups and open problems in the field.
Findings
Cannon-Thurston maps link complex analysis and hyperbolic geometry.
The paper sketches connections to hyperbolic subgroups.
It identifies open questions in the theory.
Abstract
We give an overview of the theory of Cannon-Thurston maps which forms one of the links between the complex analytic and hyperbolic geometric study of Kleinian groups. We also briefly sketch connections to hyperbolic subgroups of hyperbolic groups and end with some open questions.
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