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Journal Articles Annales Henri Lebesgue Year : 2020

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

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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Dates and versions

hal-04369516 , version 1 (02-01-2024)

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Marc Bourdon, Bertrand Rémy. Quasi-isometric invariance of continuous group L p -cohomology, and first applications to vanishings. Annales Henri Lebesgue, 2020, 3, pp.1291-1326. ⟨10.5802/ahl.61⟩. ⟨hal-04369516⟩
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