Topological and geometric restrictions on hyperconvex representations

James Farre; Beatrice Pozzetti; Gabriele Viaggi

doi:10.1515/crelle-2025-0047

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arXiv · 2403.13668

Topological and geometric restrictions on hyperconvex representations

James Farre·Beatrice Pozzetti·Gabriele Viaggi

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Abstract

We study the geometry of hyperconvex representations of hyperbolic groups in ${\rm PSL}(d,\mathbb{C})$ 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 $2$.

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James Farre, Beatrice Pozzetti, Gabriele Viaggi. 2024-03-20. Topological and geometric restrictions on hyperconvex representations. https://doi.org/10.1515/crelle-2025-0047

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