Affine laminations and coaffine representations

2024/04/22 by Martin Bobb, Bobb, M. D., James Farre +1 · 1 citation
Engineering · #Composite Structure Analysis and Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mechanical Behavior of Composites #Structural Analysis of Composite Materials

paper · pdf · doi:10.48550/arxiv.2404.14284

openalex publication_date 2024/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study surface subgroups of SL(4,\mathbb R) acting convex cocompactly on \mathbb R \textrm P³ with image in the coaffine group. The boundary of the convex core is stratified, and the one dimensional strata form a pair of bending laminations. We show that the bending data on each component consist of a convex \mathbb R \textrm P² structure and an affine measured lamination depending on the underlying convex projective structure on S with (Hitchin) holonomy ρ: π₁S → SL(3,\mathbb R). We study the space \mathcal ML^ρ(S) of bending data compatible with ρ and prove that its projectivization is a sphere of dimension 6g-7.

Cited by

• Kleinian viewpoints on higher rank worlds

Related

• On a stratification of the space of (projective) measured laminations
• Realisation of bending measured laminations by Kleinian surface groups
• d-pleated surfaces and their shear-bend coordinates
• Laminations in holomorphic dynamics
• d‐Pleated surfaces and their shear‐bend coordinates