Primitive stable representations of free Kleinian groups

TL;DR

This paper establishes a complete criterion for primitive stability of discrete faithful representations of free Kleinian groups, resolving conjectures about geometric conditions in hyperbolic 3-manifolds.

Contribution

It provides a full characterization of primitive stable representations of free Kleinian groups, answering longstanding conjectures.

Findings

Complete criterion for primitive stability

Resolution of Minsky's conjectures

Geometric conditions linked to stability

Abstract

In this paper, we give a complete criterion for a discrete faithful representation $\rho:F_n \ra \pslc$ to be primitive stable. This will answer Minsky's conjectures about geometric conditions on $\H^3/\rho(F_n)$ regarding the primitive stability of $\rho$.