NON-VANISHING FOR GROUP L^p -COHOMOLOGY ...
Document type :
Pré-publication ou Document de travail
Title :
NON-VANISHING FOR GROUP L^p -COHOMOLOGY OF SOLVABLE AND SEMISIMPLE LIE GROUPS
Author(s) :
Bourdon, Marc [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rémy, Bertrand [Auteur]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
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Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rémy, Bertrand [Auteur]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
English keyword(s) :
L^p -cohomology
Lie group
symmetric space
quasi-isometric invariance
spectral sequence
cohomology (non-)vanishing
root system
Lie group
symmetric space
quasi-isometric invariance
spectral sequence
cohomology (non-)vanishing
root system
HAL domain(s) :
Mathématiques [math]/Théorie des groupes [math.GR]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Géométrie différentielle [math.DG]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
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Anglais
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