Weakly positive and directed Anosov representations

DOI10.1016/J.AIM.2022.108611arXiv2008.02424MaRDI QIDQ6346580

Tengren Zhang, Sungwoon Kim, Ser Peow Tan

Publication date: 5 August 2020

Abstract: Given a finitely generated group $Gamma$, a directed graph $Lambda$, and a map $R:LambdaoGamma$, 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 $mathrmPGL(V)$, including non-discrete and non-faithful examples.

Mathematics Subject Classification ID

Free nonabelian groups (20E05) Group actions on manifolds and cell complexes in low dimensions (57M60) Projective representations and multipliers (20C25)

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