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arXiv · 2112.05386

Cataclysms for Anosov representations

Mareike Pfeil
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Abstract

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

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Mareike Pfeil. 2022-08-21. Cataclysms for Anosov representations. https://doi.org/10.1007/s10711-022-00721-7

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