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.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)