Compactification d’espaces de représentations de groupes de type fini
By Anne Parreau. Mathematische Zeitschrift, 2010
55 citations recorded by the source corpus.
Let Γ be a finitely generated group and G be a noncompact semisimple connected real Lie group with finite center. We consider the space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript X(\Gamma, G)}$$\end{document} of conjugacy classes of semisimple representations of Γ into G, which is the maximal Hausdorff quotient of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm Hom}(\Gamma, G)/G}$$\end{document} . We define the translation vector of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g \in G}$$\end{document}, with value in a Weyl chamber, as a natural refinement of the translation length of g in the symmetric space associated with G. We construct a compactification of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript X(\Gamma, G)}$$\end{document} , induced by the marked translation vector spectrum, generalizing Thurston’s compactification of the Teichmüller space. We show that the boundary points are projectivized marked translation vector spectra of actions of Γ on affine buildings with no global fixed point. An analoguous result holds for any reductive group G over a local field.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/75c952251356cee3bd558511719332b7fcbd4aa2
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- AN INVITATION TO HIGHER TEICHMÜLLER THEORY (2019, unknown): “Anne Parreau (2012).”
- An invitation to higher Teichm\"uller theory (2018, background): “In [26] Burger, Iozzi, Parreau and Pozzetti establish a new decomposition theorem for geodesic currents, which will play a crucial role in their program to understand the marked length spectrum compactification of maximal representations.”