Vanishing of the first reduced cohomology with values in an \(L^p\)-representation

DOI10.5802/aif.2449zbMath1225.22019arXivmath/0611001OpenAlexW4302035158MaRDI QIDQ1013033

Romain Tessera

Publication date: 29 April 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611001

zbMATH Keywords

homogeneous Riemannian manifoldhyperbolic metric spacesamenable groupsFølner sequencesreduced \(L^p\)-cohomology

Mathematics Subject Classification ID

Geometric group theory (20F65) Homogeneous spaces (22F30) Harmonic analysis on homogeneous spaces (43A85) Unitary representations of locally compact groups (22D10) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (12)

Harmonic functions with finite \(p\)-energy on lamplighter graphs are constant ⋮ \(L^p\)-cohomology in degree 1 of homogeneous spaces ⋮ Topologizing Lie algebra cohomology ⋮ Non-vanishing for group \(L^p\)-cohomology of solvable and semisimple Lie groups ⋮ Relative L^p-cohomology and application to Heintze groups ⋮ Quasi-isometric invariance of continuous group \(L^p\)-cohomology, and first applications to vanishings ⋮ Contracting automorphisms and \(L^p\)-cohomology in degree one ⋮ Vanishing of ℓ^p-cohomology and transportation cost ⋮ On the vanishing of reduced 1-cohomology for Banach representations ⋮ Large scale Sobolev inequalities on metric measure spaces and applications ⋮ Linear and Nonlinear Harmonic Boundaries of Graphs; An Approach with ℓ p-Cohomology in Degree One ⋮ Unnamed Item

Cites Work

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• Croissance polynomiale et périodes des fonctions harmoniques
• 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations
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