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arXiv · 2405.14658

Proper affine deformations of positive representations

Jean-Philippe Burelle·Neža Žager Korenjak
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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.

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Jean-Philippe Burelle, Neža Žager Korenjak. 2024-05-23. Proper affine deformations of positive representations. https://arxiv.org/abs/2405.14658

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