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arXiv · 2103.14875

Modular orbits on the representation spaces of compact abelian Lie groups

Yohann Bouilly·Gianluca Faraco
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Abstract

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 $\Bbb T^n$-character variety giving necessary and sufficient conditions for 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.

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Yohann Bouilly, Gianluca Faraco. 2021-03-27. Modular orbits on the representation spaces of compact abelian Lie groups. https://arxiv.org/abs/2103.14875

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