DE RHAM L p -COHOMOLOGY FOR HIGHER RANK SPACES AND GROUPS: CRITICAL EXPONENTS AND RIGIDITY - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

DE RHAM L p -COHOMOLOGY FOR HIGHER RANK SPACES AND GROUPS: CRITICAL EXPONENTS AND RIGIDITY

Résumé

We initiate the investigation of critical exponents (in degree equal to the rank) for the vanishing of L p-cohomology of higher rank Lie groups and related manifolds. We deal with the rank 2 case and exhibit such phenomena for SL 3 (R) and for a family of 5-dimensional solvable Lie groups. This leads us to exhibit a continuum of quasi-isometry classes of rank 2 solvable Lie groups of non-positive curvature. We provide a detailed description of the L p-cohomology of the real and complex hyperbolic spaces, to be combined with a spectral sequence argument for our higher-rank results.
Fichier principal
Vignette du fichier
L^pNPC.pdf (247.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04369541 , version 1 (02-01-2024)

Identifiants

Citer

Marc Bourdon, Bertrand Rémy. DE RHAM L p -COHOMOLOGY FOR HIGHER RANK SPACES AND GROUPS: CRITICAL EXPONENTS AND RIGIDITY. 2023. ⟨hal-04369541⟩
5 Consultations
12 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More