(d\)-pleated surfaces and their shear-bend coordinates

In this article, we single out representations of surface groups into \(\mathsf{PSL}_d(\mathbb{C})\) which generalize the well-studied family of pleated surfaces into \(\mathsf{PSL}_2(\mathbb{C})\). Our representations arise as sufficiently generic \(\lambda\)-Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination \(\lambda\). For fixed \(\lambda\) and \(d\), we provide a holomorphic parametrization of the space \(\mathcal{R}(\lambda,d)\) of \((\lambda,d)\)-pleated surfaces which extends both work of Bonahon for pleated surfaces and Bonahon and Dreyer for Hitchin representations.