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Boundary of Anosov coaffine representations
Abstract
Let Γ≤ SL(d+1,ℝ) be a torsion-free hyperbolic group dividing a properly and strictly convex domain Ω⊂ ℝPd, and let ρ: Γ→ SL(d+1,ℝ) be the inclusion. We study representations of Γ into the coaffine group that are deformations of ρ⊕ 1 ∈ Hom(Γ, GL(d+2,ℝ)) and that lie on the boundary of the locus of projective Anosov representations. In this setting, we identify a canonical limit set Λ for the action and study its fine geometric features which are, in a suitable sense, stable. We prove the existence of an ending lamination that encodes the failure of the Anosov condition and the non-existence of a Cannon--Thurston map. Under certain conditions, we compute the Hausdorff dimension and show that the corresponding measure is positive.
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BibTeX
@misc{bobb2026boundary,
title = {{Boundary of Anosov coaffine representations}},
author = {Marit Bobb and James Farre},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14897},
eprint = {2610.14897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14897},
}
RIS
TY - UNPB
TI - Boundary of Anosov coaffine representations
AU - Marit Bobb
AU - James Farre
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14897
UR - https://arxiv.org/abs/2610.14897
AB - Let Γ≤ SL(d+1,ℝ) be a torsion-free hyperbolic group dividing a properly and strictly convex domain Ω⊂ ℝP^d, and let ρ: Γ→ SL(d+1,ℝ) be the inclusion. We study representations of Γ into the coaffine group that are deformations of ρ⊕ 1 ∈ Hom(Γ, GL(d+2,ℝ)) and that lie on the boundary of the locus of projective Anosov representations. In this setting, we identify a canonical limit set Λ for the action and study its fine geometric features which are, in a suitable sense, stable. We prove the existence of an ending lamination that encodes the failure of the Anosov condition and the non-existence of a Cannon--Thurston map. Under certain conditions, we compute the Hausdorff dimension and show that the corresponding measure is positive.
ER -