Anosov representations with Lipschitz limit set

• Verfasst von: Pozzetti, Maria Beatrice [VerfasserIn]
• Verfasst von: Sambarino, Andrés [VerfasserIn]
• Verfasst von: Wienhard, Anna [VerfasserIn]
• Titel: Anosov representations with Lipschitz limit set
• Verf.angabe: Maria Beatrice Pozzetti, Andrés Sambarino, Anna Wienhard
• E-Jahr: 2023
• Jahr: 9 November 2023
• Umfang: 58 S.
• Fussnoten: Gesehen am 10.01.2024
• Titel Quelle: Enthalten in: Geometry & topology
• Ort Quelle: Berkeley, Calif. : Mathematical Sciences Publishers, 1997
• Jahr Quelle: 2023
• Band/Heft Quelle: 27(2023), 8, Seite 3303-3360
• ISSN Quelle: 1364-0380
• DOI: doi:10.2140/gt.2023.27.3303
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1877628247

Abstract

We study Anosov representations whose limit set has intermediate regularity, namely is a Lipschitz submanifold of a flag manifold. We introduce an explicit linear functional, the unstable Jacobian, whose orbit growth rate is integral on this class of representations. We prove that many interesting higher-rank representations, including Θ-positive representations, belong to this class, and establish several applications to rigidity results on the orbit growth rate in the symmetric space.