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d‐Pleated surfaces and their shear‐bend coordinates

2026/06/30 by Sara Maloni, Giuseppe Martone, Filippo Mazzoli +1
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.1112/plms.70174

Abstract

Abstract In this article, we single out representations of surface groups into that generalize the well‐studied family of pleated surfaces into . Our representations arise as sufficiently generic ‐Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination . For fixed and , we provide a holomorphic parameterization of the space of ‐pleated surfaces with pleating locus that extends both work of Bonahon for pleated surfaces and Bonahon and Dreyer for Hitchin representations.

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