Modular orbits on the representation spaces of compact abelian Lie groups (Q6039667)

Summary: 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 \(\mathbb{T}^n\)-character variety giving necessary and sufficient conditions for \(\operatorname{Mod} (S)\)-orbits to be dense. As an application, such a characterisation provides a dynamical proof of the Kronecker's theorem concerning inhomogeneous Diophantine approximation.