Positive crossratios, barycenters, trees and applications to maximal representations
Abstract
We study metric properties of maximal framed representations of fundamental groups of surfaces in symplectic groups over real closed fields, interpreted as actions on Bruhat-Tits buildings endowed with adapted Finsler norms. We prove that the translation length can be computed as intersection with a geodesic current, give sufficient conditions guaranteeing that such a current is a multicurve, and, if the current is a measured lamination, construct an isometric embedding of the associated tree in the building. These results are obtained as application of more general results of independent interest on positive crossratios and actions with compatible barycenters.
Keywords
Cite
@article{arxiv.2103.17161,
title = {Positive crossratios, barycenters, trees and applications to maximal representations},
author = {Marc Burger and Alessandra Iozzi and Anne Parreau and Maria Beatrice Pozzetti},
journal= {arXiv preprint arXiv:2103.17161},
year = {2021}
}
Comments
Comments are welcome! v2 Expanded and corrected version of the example in Section 8.3, definition of the period of a crossratio expanded, several minor corrections in the whole paper