English

Modular orbits on the representation spaces of compact abelian Lie groups

Dynamical Systems 2022-03-18 v2 Geometric Topology Number Theory

Abstract

Let SS be a closed surface of genus gg greater than zero. In the present paper we study the topological-dynamical action of the mapping class group on the Tn\Bbb T^n-character variety giving necessary and sufficient conditions for Mod(S)(S)-orbits to be dense. As an application, such a characterisation provides a dynamical proof of the Kronecker's Theorem concerning inhomogeneous diophantine approximation.

Keywords

Cite

@article{arxiv.2103.14875,
  title  = {Modular orbits on the representation spaces of compact abelian Lie groups},
  author = {Yohann Bouilly and Gianluca Faraco},
  journal= {arXiv preprint arXiv:2103.14875},
  year   = {2022}
}

Comments

18 pages. Final version accepted at Groups, Geometry and Dynamics

R2 v1 2026-06-24T00:36:35.970Z