d-pleated surfaces and their shear-bend coordinates

2023/05/19 by Maloni, Sara, Martone, Giuseppe, Mazzoli, Filippo +1 · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2305.11780

Abstract

In this article, we single out representations of surface groups into PSL_d(ℂ) which generalize the well-studied family of pleated surfaces into PSL₂(ℂ). Our representations arise as sufficiently generic λ-Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination λ. For fixed λ and d, we provide a holomorphic parametrization of the space R(λ,d) of (λ,d)-pleated surfaces which extends both work of Bonahon for pleated surfaces and Bonahon and Dreyer for Hitchin representations.

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• d‐Pleated surfaces and their shear‐bend coordinates
• Topology of the space of d-pleated surfaces
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• Geometry of hyperconvex representations of surface groups
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