Affine laminations and coaffine representations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929523166019584 |
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| author | Bobb, M. D. Farre, James |
| author_facet | Bobb, M. D. Farre, James |
| contents | We study surface subgroups of $\mathrm{SL}(4,\mathbb R)$ acting convex cocompactly on $\mathbb R \textrm P^3$ 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 $\mathbb R \textrm P^2$ structure and an affine measured lamination depending on the underlying convex projective structure on $S$ with (Hitchin) holonomy $ρ: π_1S \to \mathrm{SL}(3,\mathbb R)$. We study the space $\mathcal {ML}^ρ(S)$ of bending data compatible with $ρ$ and prove that its projectivization is a sphere of dimension $6g-7$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_14284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine laminations and coaffine representations Bobb, M. D. Farre, James Geometric Topology Dynamical Systems We study surface subgroups of $\mathrm{SL}(4,\mathbb R)$ acting convex cocompactly on $\mathbb R \textrm P^3$ 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 $\mathbb R \textrm P^2$ structure and an affine measured lamination depending on the underlying convex projective structure on $S$ with (Hitchin) holonomy $ρ: π_1S \to \mathrm{SL}(3,\mathbb R)$. We study the space $\mathcal {ML}^ρ(S)$ of bending data compatible with $ρ$ and prove that its projectivization is a sphere of dimension $6g-7$. |
| title | Affine laminations and coaffine representations |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2404.14284 |