Work

Topological and geometric restrictions on hyperconvex representations

Year: 2025

Type: article

Abstract: We study the geometry of hyperconvex representations of hyperbolic groups in PSL ⁢ ( d , C ) \mathrm{PSL}(d,\mathbb{C}) and establish two structural results: a group admitting a hyperconvex representation is virtually isomorphic to a Kleinian group, and its hyperconvex limit set in the appropriate flag manifold has Hausdorff dimension strictly smaller than 2.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0047

Authors: James Farre, Beatrice Pozzetti, Gabriele Viaggi

Institutions: Max Planck Institute for Mathematics in the Sciences, University of Bologna, Sapienza University of Rome

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G1620761618, Diskrete Untergruppen von halbeinfachen LieGruppen jenseits von Anosovdarstellungen, G6020302423, TRR 191: Symplektische Strukturen in Geometrie, Algebra und Dynamik, EXC 2181: STRUKTUREN: Emergenz in Natur, Mathematik und komplexen Daten