Appears in collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

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.