Geometry of hyperconvex representations of surface groups

James Farre; Beatrice Pozzetti; Gabriele Viaggi

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arXiv · 2407.20071

Geometry of hyperconvex representations of surface groups

James Farre·Beatrice Pozzetti·Gabriele Viaggi

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Abstract

We study the geometry of hyperconvex representations of surface groups in ${\rm PSL}(d,\mathbb{C})$ and their deformation spaces: We produce a natural holomorphic extension of the classical Ahlfors--Bers map to a product of Teichm\"uller spaces of a canonical Riemann surface lamination and prove that the limit set of a hyperconvex representation in the full flag space has Hausdorff dimension 1 if and only if the representation is conjugate in ${\rm PSL}(d,\mathbb{R})$.

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James Farre, Beatrice Pozzetti, Gabriele Viaggi. 2024-07-29. Geometry of hyperconvex representations of surface groups. https://arxiv.org/abs/2407.20071

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