Tangent bundles of hyperbolic spaces and proper affine actions on L^p spaces

2019/01/22 by Indira Chatterji, Chatterji, Indira, François Dahmani +5
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1901.07462

openalex publication_date 2019/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the notion of a negatively curved tangent bundle of a metric measured space. We prove that, when a group G acts on a metric measured space X with a negatively curved tangent bundle, then G acts on some L^p space, and that this action is proper under suitable assumptions. We then check that this result applies to the case when X is a hyperbolic space.

Related

• Hyperbolic groups admit proper affine isometric actions on l^p-spaces
• On negatively curved bundles with hyperbolic fibers outside the Igusa stable range
• The Teichmüller Space of Pinched Negatively Curved Metrics on a Hyperbolic Manifold is not Contractible
• Warped cones and proper affine isometric actions of discrete groups on Banach spaces
• Central extensions and proper actions on products of hyperbolic spaces