Zariski-dense surface groups in non-uniform lattices of split real Lie groups

2022/06/02 by Jacques Audibert, Audibert, Jacques
Mathematics · #22E40 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2206.01123

openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For \textrmSL(n,ℝ) (n≥3), \textrmSO(n+1,n) (n≥2), \textrmSp(2n,ℝ) (n≥2) and for the adjoint real split form of the exceptional group \textrmG₂, we exhibit non-uniform lattices in which we construct thin Hitchin representations by arithmetic methods. These representations give infinitely many orbits under the action of the mapping class group (except maybe for \textrmG₂). In particular, we show that when p≠2 is prime every non-uniform lattice of SL(p,ℝ) contains thin Hitchin representations.

Related

• Zariski-dense Hitchin representations in uniform lattices
• Zariski dense surface subgroups in SL(n,ℚ) with odd n
• Most Hitchin representations are strongly dense
• Integral Zariski dense surface groups in SL(n,R)
• A hyperbolic lattice in each dimension with Zariski-dense surface subgroups