Cataclysms for Anosov representations

Abstract

In this paper, we construct cataclysm deformations for $\theta$-Anosov representations into a semisimple non-compact connected real Lie group $G$ with finite center, where $\theta \subset \Delta$ is a subset of the simple roots that is invariant under the opposition involution. These generalize Thurston's cataclysms on Teichmüller space and Dreyer's cataclysms for Borel-Anosov representations into $\mathrm{PSL}(n,\mathbb{R})$. We express the deformation also in terms of the boundary map. Furthermore, we show that cataclysm deformations are additive and behave well with respect to composing a representation with a group homomorphism. Finally, we show that the deformation is injective for Hitchin representations, but not in general for $\theta$-Anosov representations.

32 pages, 3 figures; small changes as response to reviewer's comments. Accepted for publication in Geometriae Dedicata - the Version of Record is available online at: http://dx.doi.org/10.1007/s10711-022-00721-7

References in corpus (1)

• Topological restrictions on Anosov representations