Cataclysms for Anosov representations

• Verfasst von: Pfeil, Mareike [VerfasserIn]
• Titel: Cataclysms for Anosov representations
• Verf.angabe: Mareike Pfeil
• E-Jahr: 2022
• Jahr: 17 August 2022
• Umfang: 31 S.
• Fussnoten: Gesehen am 09.09.2022
• Titel Quelle: Enthalten in: Geometriae dedicata
• Ort Quelle: Dordrecht [u.a.] : Springer Science + Business Media B.V, 1972
• Jahr Quelle: 2022
• Band/Heft Quelle: 216(2022), 6, Artikel-ID 61, Seite 1-31
• ISSN Quelle: 1572-9168
• DOI: doi:10.1007/s10711-022-00721-7
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Anosov representations
• Sach-SW: Cataclysms
• Sach-SW: Discrete subgroups of Lie groups
• Sach-SW: surface groups
• K10plus-PPN: 1816348767
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

In this paper, we construct cataclysm deformations for theta-Anosov representations into a semisimple non-compact connected real Lie group G with finite center, where theta subset of Lambda is a subset of the simple roots that is invariant under the opposition involution. These generalize Thurston's cataclysms on Teichmiiller 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 arc 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 theta-Anosov representations.