Cataclysms for Anosov representations

Abstract

AbstractIn this paper, we construct cataclysm deformations for $$\theta $$ θ -Anosov representations into a semisimple non-compact connected real Lie group G with finite center, where $$\theta \subset \Delta $$ θ ⊂ Δ 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 $$\mathrm {PSL}(n, \mathbb {R})$$ PSL ( n , 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 $$\theta $$ θ -Anosov representations.