Bibliographic Details
| Title: |
d‐Pleated surfaces and their shear‐bend coordinates. |
| Authors: |
Maloni, Sara1 (AUTHOR), Martone, Giuseppe2 (AUTHOR), Mazzoli, Filippo3 (AUTHOR) filippo.mazzoli@ucr.edu, Zhang, Tengren4 (AUTHOR) |
| Source: |
Proceedings of the London Mathematical Society. Jul2026, Vol. 133 Issue 1, p1-147. 147p. |
| Subject Terms: |
*Representations of groups (Algebra), *Parameterization, *Curved surfaces |
| Abstract: |
In this article, we single out representations of surface groups into PGLd(C)$\mathsf {PGL}_d(\mathbb {C})$ that generalize the well‐studied family of pleated surfaces into PGL2(C)$\mathsf {PGL}_2(\mathbb {C})$. Our representations arise as sufficiently generic λ$\lambda$‐Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination λ$\lambda$. For fixed λ$\lambda$ and d$d$, we provide a holomorphic parameterization of the space Rd(λ)$\mathcal {R}_d(\lambda)$ of d$d$‐pleated surfaces with pleating locus λ$\lambda$ that extends both work of Bonahon for pleated surfaces and Bonahon and Dreyer for Hitchin representations. [ABSTRACT FROM AUTHOR] |
| Database: |
Academic Search Index |