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Pré-Publication, Document De Travail Année : 2021

NON-VANISHING FOR GROUP L^p -COHOMOLOGY OF SOLVABLE AND SEMISIMPLE LIE GROUPS

Marc Bourdon

Résumé

We obtain non-vanishing of group L^p-cohomology of Lie groups for p large and when the degree is equal to the rank of the group. This applies both to semisimple and to some suitable solvable groups. In particular, it confirms that Gromov's question on vanishing below the rank is formulated optimally. To achieve this, some complementary vanishings are combined with the use of spectral sequences. To deduce the semisimple case from the solvable one, we also need comparison results between various theories for L^p-cohomology, allowing the use of quasi-isometry invariance.
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Dates et versions

hal-03347474 , version 1 (17-09-2021)

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  • HAL Id : hal-03347474 , version 1

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Marc Bourdon, Bertrand Rémy. NON-VANISHING FOR GROUP L^p -COHOMOLOGY OF SOLVABLE AND SEMISIMPLE LIE GROUPS. 2021. ⟨hal-03347474⟩
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