On the ℓ q,p cohomology of Carnot groups
[Sur la cohomologie ℓ q,p des groupes de Carnot]
Pansu, Pierre1 ; Rumin, Michel1
1 Laboratoire de Mathématiques d’Orsay Université Paris-Sud, CNRS Université Paris-Saclay, 91405 Orsay (France)
Annales Henri Lebesgue, Tome 1 (2018), pp. 267-295.

On étudie la cohomologie ℓ q,p des groupes de Carnot. On démontre qu’elle s’annule (ou non) suivant la position des exposants (p,q) par rapport aux poids présents dans la cohomologie de l’algèbre de Lie.

We study the simplicial ℓ q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p,q) gap with respect to the weight gaps in the Lie algebra cohomology of G.

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DOI : 10.5802/ahl.8
Classification : 20F65, 22E30, 32V20, 58J40, 35R03, 20J06, 57T10, 47B06, 43A85
Mots clés : $\ell ^{q,p}$ cohomology, Carnot group, global analysis on manifolds
Pansu, Pierre 1 ; Rumin, Michel 1

1 Laboratoire de Mathématiques d’Orsay Université Paris-Sud, CNRS Université Paris-Saclay, 91405 Orsay (France) 
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     title = {On the $\ell ^{q,p}$ cohomology of {Carnot} groups},
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     pages = {267--295},
     publisher = {\'ENS Rennes},
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     year = {2018},
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Pansu, Pierre; Rumin, Michel. On the $\ell ^{q,p}$ cohomology of Carnot groups. Annales Henri Lebesgue, Tome 1 (2018), pp. 267-295. doi : 10.5802/ahl.8. http://www.numdam.org/articles/10.5802/ahl.8/

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