Cataclysms for Anosov representations

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 ⊂ Δ is a subset of the simple roots that is invariant under the opposition involution. These generalize Thurston’s cataclysms on Teich...

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Veröffentlicht in:Geometriae dedicata 2022-12, Vol.216 (6), Article 61
1. Verfasser: Pfeil, Mareike
Format: Artikel
Sprache:eng
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Zusammenfassung: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 ⊂ 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 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 θ -Anosov representations.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-022-00721-7