Convergence groups are not invariably generated

TL;DR

This paper proves that convergence groups, a broad class including hyperbolic groups, are not invariably generated, confirming a conjecture that such groups lack this property.

Contribution

It extends the non-invariable generation property from hyperbolic groups to the more general class of convergence groups.

Findings

Convergence groups are not invariably generated.

Supports the conjecture for a larger class of groups.

Generalizes previous results on hyperbolic groups.

Abstract

It was conjectured in [KLS14] that non-elementary word hyperbolic groups are never invariably generated. We show that this is indeed the case even for the much larger class of convergence groups.