Polynomial effective density in quotients of \mathbb H³ and \mathbb H²×\mathbb H²

2021/12/29 by Lindenstrauss, Elon, Mohammadi, Amir
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2112.14562

Abstract

We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL₂(\mathbb R) in arithmetic quotients of SL₂(\mathbb C) and SL₂(\mathbb R)\timesSL₂(\mathbb R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

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