Topological and geometric restrictions on hyperconvex representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908469679882240 |
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| author | Farre, James Pozzetti, Beatrice Viaggi, Gabriele |
| author_facet | Farre, James Pozzetti, Beatrice Viaggi, Gabriele |
| contents | 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 $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological and geometric restrictions on hyperconvex representations Farre, James Pozzetti, Beatrice Viaggi, Gabriele Geometric Topology Differential Geometry Group Theory 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 $2$. |
| title | Topological and geometric restrictions on hyperconvex representations |
| topic | Geometric Topology Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2403.13668 |