Uniformization of compact complex manifolds by Anosov representations

We study uniformization problems for compact manifolds that arise as quotients of domains in complex flag varieties by images of Anosov homomorphisms. We focus on Anosov homomorphisms with "small" limit sets, as measured by the Riemannian Hausdorff codimension in the flag variety. Under su...

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Hauptverfasser: Dumas, David (VerfasserIn) , Sanders, Andrew (VerfasserIn)
Dokumenttyp: Article (Journal) Kapitel/Artikel
Sprache:Englisch
Veröffentlicht: 7 Jun 2021
Ausgabe:Version v2
In: Arxiv
Year: 2021, Pages: 1-37
DOI:10.48550/arXiv.2010.05147
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.48550/arXiv.2010.05147
Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2010.05147
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Verfasserangaben:David Dumas and Andrew Sanders
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Zusammenfassung:We study uniformization problems for compact manifolds that arise as quotients of domains in complex flag varieties by images of Anosov homomorphisms. We focus on Anosov homomorphisms with "small" limit sets, as measured by the Riemannian Hausdorff codimension in the flag variety. Under such a codimension hypothesis, we show that all first-order deformations of complex structure on the associated compact complex manifolds are realized by deformations of the Anosov homomorphism. With some mild additional hypotheses we show that the character variety maps locally homeomorphically to the (generalized) Teichm\"uller space of the manifold. In particular this provides a local analogue of the Bers Simultaneous Uniformization Theorem in the setting of Anosov homomorphisms to higher-rank complex semisimple Lie groups.
Beschreibung:Online veröffentlicht am 11. Oktober 2020
Gesehen am 10.01.2024
Beschreibung:Online Resource
DOI:10.48550/arXiv.2010.05147