Geodesic
Modular orbits on the representation spaces of compact abelian Lie groups
Yohann Bouilly1 ; Gianluca Faraco2
1Université de Strasbourg, France
2Max-Planck-Institut für Mathematik, Bonn, Germany
Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 719-749

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DOI

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 Tn-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.
DOI : 10.4171/ggd/716
Classification : 57-XX, 11-XX
Mots-clés : Mapping class group, character variety, dense representations, abelian Lie groups

Yohann Bouilly  1   ; Gianluca Faraco  2

1 Université de Strasbourg, France
2 Max-Planck-Institut für Mathematik, Bonn, Germany 
Yohann Bouilly; Gianluca Faraco. Modular orbits on the representation spaces of compact abelian Lie groups. Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 719-749. doi: 10.4171/ggd/716
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