Quasi-isometric invariance of continuous group L p -cohomology, and first applications to vanishings
Annales Henri Lebesgue, Volume 3 (2020) , pp. 1291-1326.

Metadata

KeywordsL p -cohomology, topological group, Lie group, symmetric space, quasi-isometric invariance, spectral sequence, cohomology vanishing, root system

Abstract

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.


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