Proper affine deformations of positive representations
Abstract
We define for every positive Anosov representation of a nonabelian free group into $\mathrm{SO}(2n,2n-1)$ a family of $\mathbb{R}^{4n-1}$-valued cocycles which induce proper affine actions on $\mathbb{R}^{4n-1}$. We construct fundamental domains in $\mathbb{R}^{4n-1}$ bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.14658
- arXiv:
- arXiv:2405.14658
- Bibcode:
- 2024arXiv240514658B
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Geometric Topology;
- 22E40;
- 20H10
- E-Print:
- 23 pages, 2 figures