Compactification d'espaces de représentations de groupes de type fini
Abstract
Let $\Gamma$ be a finitely generated group and $G$ be a noncompact semisimple connected real Lie group with finite center. We consider the space $\mathcal X$ of conjugacy classes of reductive representations of $\Gamma$ into $G$. We define the {\it translation vector} of an element $g$ in $G$, with values in a Weyl chamber, as a refinement of the translation length in the associated symmetric space. We construct a compactification of $\mathcal X$, 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 $\Gamma$ on affine buildings with no global fixed point. An analoguous result holds for any reductive group $G$ over a local field.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.1111
 Bibcode:
 2010arXiv1003.1111P
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Group Theory;
 Mathematics  Metric Geometry
 EPrint:
 40 pages