Let be a closed surface of genus greater than zero. In the present paper, we study the topological-dynamical action of the mapping class group on the -character variety giving necessary and sufficient conditions for -orbits to be dense. As an application, such a characterisation provides a dynamical proof of the Kronecker's theorem concerning inhomogeneous Diophantine approximation.
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Yohann Bouilly, Gianluca Faraco, Modular orbits on the representation spaces of compact abelian Lie groups. Groups Geom. Dyn. 17 (2023), no. 2, pp. 719–749DOI 10.4171/GGD/716