Modular orbits on the representation spaces of compact abelian Lie groups

2021/03/27 by Yohann Bouilly, Gianluca Faraco, Bouilly, Yohann +1
Mathematics · #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.14875

openalex publication_date 2021/03/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let S be a closed surface of genus g greater than zero. In the present paper we study the topological-dynamical action of the mapping class group on the \Bbb Tⁿ-character variety giving necessary and sufficient conditions for Mod(S)-orbits to be dense. As an application, such a characterisation provides a dynamical proof of the Kronecker's Theorem concerning inhomogeneous diophantine approximation.

Related

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