Modular orbits on the representation spaces of compact abelian Lie groups

[摘要] Let SSS be a closed surface of genus ggg greater than zero. In the present paper, we study the topological-dynamical action of the mapping class group on the Tn\mathbb T^nTn-character variety giving necessary and sufficient conditions for Mod(S)\mathrm{Mod}(S)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.

[学科分类] 神经科学

[关键词] Mapping class group;character variety;dense representations;abelian Lie groups