published on May 19, 2025
Deformations of Barbot representations into $\textrm{SL}(3,\mathbb{R})$
By Colin Davalo
Proper affine deformations of positive representations
For every positive Anosov representation of a free group into $\mathrm{SO}(2n,2n-1)$, we define a family of cocycles giving rise to proper affine actions with the given linear part on $4n-1$--dimensional real affine space. Furthermore, we use higher-dimensional versions of Drumm's crooked planes to construct fundamental domains for these actions. This is joint work with Jean-Philippe Burelle.
