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 |
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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. |
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ISSN: | 0046-5755 1572-9168 |
DOI: | 10.1007/s10711-022-00721-7 |