Séminaire Géométrie et groupes discrets

Geodesic Currents, Positive Cross-Ratios and Degenerations of Maximal Representations

by Prof. Anne Parreau (Université Grenoble Alpes)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Degenerations of maximal representations of a surface group may be seen as maximal representations in Sp(2n,F) for some non-Archimedean real closed field F. We associate to every such maximal representation a geodesic current whose intersection number is the length function of the representation for the L1 norm. When  the current is a measured lamination, we reconstruct an equivariant isometric embedding of the dual real tree in the Bruhat-Tits  building of Sp(2n,F).  This involves a general construction of an intersection current associated to a non necessarily continuous positive cross-ratio.

This is joint work with Marc Burger, Alessandra Iozzi, and Beatrice Pozzetti.