Bouilly, Yohann and Faraco, Gianluca (2021) Modular orbits on the representation spaces of compact abelian Lie groups. MPIM Preprint Series 2021 (13).
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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 $\mathbb{T}^n$-character variety giving necessary and sufficient conditions for $\text{Mod}(S)$-orbits to be dense. As an application, such a characterisation provides a dynamical proof of the Kronecker's Theorem concerning inhomogeneous diophantine approximation.
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 3 Geometry and topology > 57-XX Manifolds and cell complexes |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 23 Apr 2021 10:28 |
| Last Modified: | 18 May 2021 11:09 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4541 |
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