Asymptotic Dynamics on Character Varieties over Finite Fields

2025/02/21 by Cigole Thomas, Thomas, Cigole
Mathematics · Physics and Astronomy · #14M35 #37P55 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2502.16009

openalex publication_date 2025/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the lack of asymptotic transitivity of the outer automorphism group action of ℤ^r on SL_n(\mathbbF_q)-character varieties of ℤ^r for n=2,3 and r≥ 2. Along the way, we stratify the character varieties and compute the E-polynomial, also known as the Hodge-Deligne polynomial or Serre polynomial, of these character varieties.

Related

• Dynamics on character varieties: a survey
• On the E-polynomials of a family of Character Varieties
• E-polynomials of character varieties for real curves
• On the E-polynomial of parabolic Sp_2n-character varieties
• On Hodge polynomials of Singular Character Varieties