Weakly positive and directed Anosov representations

Abstract

Given a finitely generated group $\Gamma$, a directed graph $\Lambda$, and a map $R:\Lambda \to \Gamma$, we introduce the notion of an $(R,\Lambda )$-directed Anosov representation. This is a weakening of the notion of Anosov representations. Our main theorem gives a procedure to construct $(R,\Lambda )$-directed Anosov representations using Fock-Goncharov positivity. As an application of our main theorem, we construct large families of primitive stable representations from $F_2$ to $\mathrm{PGL}(V)$, including non-discrete and non-faithful examples.

We generalize and reformulate the notions of R-directed Anosov and R-weakly positive representations in the previous manuscript. In addition, we make changes to clarify the previous manuscript

References in corpus (2)

• The Modular Group Action on Real SL(2)-characters of a One-Holed Torus
• Primitive stability and Bowditch's BQ-condition are equivalent