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September 10, 2025Journal für die reine und angewandte Mathematik (Crelles Journal)0 citations

Topological and geometric restrictions on hyperconvex representations

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JFJames FarreBPBeatrice PozzettiGVGabriele Viaggi

Key Points

  • A group with hyperconvex representation is virtually isomorphic to a Kleinian group, indicating deep geometric links.
  • The hyperconvex limit set within flag manifolds shows a Hausdorff dimension that is less than 2, emphasizing its intricate structure.
  • The study focuses on geometric aspects of hyperbolic groups represented through PSL(d,C) and their implications.
  • Findings suggest significant topological constraints on hyperconvex representations impacting geometric group theory.

Abstract

Abstract We study the geometry of hyperconvex representations of hyperbolic groups in PSL ⁢ (d, C) 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.

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Cite This Study

Farre et al. (2025) studied this question.

synapsesocial.com/papers/68c1ae6654b1d3bfb60e6191https://doi.org/10.1515/crelle-2025-0047
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