Cataclysms for Anosov representations
Abstract
In this paper, we construct cataclysm deformations for -Anosov representations into a semisimple non-compact connected real Lie group with finite center, where 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 . 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 -Anosov representations.
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