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d‐Pleated surfaces and their shear‐bend coordinates.

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Τίτλος: d‐Pleated surfaces and their shear‐bend coordinates.
Συγγραφείς: Maloni, Sara1 (AUTHOR), Martone, Giuseppe2 (AUTHOR), Mazzoli, Filippo3 (AUTHOR) filippo.mazzoli@ucr.edu, Zhang, Tengren4 (AUTHOR)
Πηγή: Proceedings of the London Mathematical Society. Jul2026, Vol. 133 Issue 1, p1-147. 147p.
Θεματικοί όροι: *Representations of groups (Algebra), *Parameterization, *Curved surfaces
Περίληψη: 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]
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  Data: d‐Pleated surfaces and their shear‐bend coordinates.
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  Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+London+Mathematical+Society%22">Proceedings of the London Mathematical Society</searchLink>. Jul2026, Vol. 133 Issue 1, p1-147. 147p.
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  Data: 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]
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        Value: 10.1112/plms.70174
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      – Code: eng
        Text: English
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        PageCount: 147
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      – SubjectFull: Representations of groups (Algebra)
        Type: general
      – SubjectFull: Parameterization
        Type: general
      – SubjectFull: Curved surfaces
        Type: general
    Titles:
      – TitleFull: d‐Pleated surfaces and their shear‐bend coordinates.
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            NameFull: Maloni, Sara
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            NameFull: Martone, Giuseppe
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            NameFull: Mazzoli, Filippo
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            NameFull: Zhang, Tengren
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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