Intersecting limit sets of Kleinian subgroups and Susskind's question

TL;DR

This paper constructs a specific Fuchsian group demonstrating a counterexample to a longstanding conjecture about the intersection properties of limit sets of subgroups, thereby resolving a question posed in 1989.

Contribution

It provides the first explicit example of a Fuchsian group with subgroups having trivial intersection but intersecting limit sets, answering Susskind's question negatively.

Findings

Constructed a non-elementary Fuchsian group with the desired properties.

Showed that the radial limit sets of the subgroups intersect non-trivially.

Negatively answered Susskind's conjecture from 1989.

Abstract

We construct a non-elementary Fuchsian group that admits two non-elementary subgroups with trivial intersection and whose radial limit sets intersect non-trivially. This negatively answers a question of Perry Susskind (1989) that was stated as a conjecture by James W. Anderson (2014).