# Bowditch's Q-conditions and Minsky's primitive stability

## TL;DR

This paper proves the equivalence of two known domains of discontinuity for the outer automorphism group action on PSL(2,C) character varieties of free groups, and relates them to characters with the bounded intersection property.

## Contribution

It establishes the equality of Bowditch's and Minsky's domains and links them to the bounded intersection property, clarifying the structure of these character varieties.

## Key findings

- Proved Bowditch's and Minsky's domains are equal.
- Showed these domains are contained in characters with the bounded intersection property.
- Enhanced understanding of the dynamics of outer automorphism group actions.

## Abstract

For the action of the outer automorphism group of the rank two free group on the corresponding variety of PSL(2,C) characters, two domains of discontinuity have been known to exist that are strictly larger than the set of Schottky characters. One is introduced by Bowditch in 1998 (followed by Tan, Wong and Zhang in 2008) and the other by Minsky in 2013. We prove that these two domains are equal. We then show that they are contained in the set of characters having what we call the bounded intersection property.