Modular orbits on the representation spaces of compact abelian Lie groups
Dynamical Systems
2022-03-18 v2 Geometric Topology
Number Theory
Abstract
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 Mod-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