Title :

Quasi-isometric invariance of continuous group L p -cohomology, and first applications to vanishings

Author(s) :

Bourdon, Marc [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rémy, Bertrand [Auteur]
Centre de Mathématiques Laurent Schwartz [CMLS]

Journal title :

Annales Henri Lebesgue

Pages :

1291-1326

Publisher :

UFR de Mathématiques - IRMAR

Publication date :

2020-11-05

ISSN :

2644-9463

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We show that the continuous L p-cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a positive answer to a question asked by M. Gromov, ...
Show more >We show that the continuous L p-cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a positive answer to a question asked by M. Gromov, suggesting a classical behaviour of continuous L p-cohomology of simple real Lie groups. In addition to quasi-isometric invariance, the ingredients are a spectral sequence argument and Pansu's vanishing results for real hyperbolic spaces. In the best adapted cases of simple Lie groups, we obtain nearly half of the relevant vanishings.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Méthodes géométriques en théorie de Lie

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL