English

Cataclysms for Anosov representations

Geometric Topology 2022-08-23 v2

Abstract

In this paper, we construct cataclysm deformations for θ\theta-Anosov representations into a semisimple non-compact connected real Lie group GG with finite center, where θΔ\theta \subset \Delta is a subset of the simple roots that is invariant under the opposition involution. These generalize Thurston's cataclysms on Teichm\"uller space and Dreyer's cataclysms for Borel-Anosov representations into PSL(n,R)\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\theta-Anosov representations.

Keywords

Cite

@article{arxiv.2112.05386,
  title  = {Cataclysms for Anosov representations},
  author = {Mareike Pfeil},
  journal= {arXiv preprint arXiv:2112.05386},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-24T08:11:55.160Z