Title :

De Rham L^p -Cohomology for Higher Rank Spaces and Groups: Critical Exponents and Rigidity

Author(s) :

Bourdon, Marc [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rémy, Bertrand [Auteur]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]

Publication date :

2023-12-21

English keyword(s) :

L^p -cohomology
Lie group
Symmetric space
Quasi-isometric invariance
Spectral sequence
Cohomology (non-)vanishing

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL