We study the geometry of hyperconvex representations of hyperbolic groups in PSL (d, 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.
Topological and geometric restrictions on hyperconvex representations / Farre, J., Pozzetti, B., Viaggi, G.. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - (2025). [10.1515/crelle-2025-0047]
Topological and geometric restrictions on hyperconvex representations
Viaggi, Gabriele
2025
Abstract
We study the geometry of hyperconvex representations of hyperbolic groups in PSL (d, 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.File allegati a questo prodotto
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