no. 3
Cohomologie ℓ p en degrés supérieurs et dimension conforme
[ℓ p -Cohomology in higher degrees and conformal dimension]
Bourdon, Marc1
1 Laboratoire Painlevé UMR CNRS 8524 Université de Lille 1 59655 Villeneuve d’Ascq (France)
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 1013-1043.

We establish a sufficient condition for vanishing of the ℓ p -cohomology of hyperbolic uniformly contractible simplicial complexes, in degree at least 2. As an application, a geometric lower bound for the conformal dimension of the boundary at infinity of some hyperbolic groups, is obtained.

On donne une condition suffisante pour l’annulation de la cohomologie ℓ p en degré supérieur à 2, des complexes simpliciaux hyperboliques uniformément contractiles. Comme application, on obtient une minoration de la dimension conforme du bord à l’infini de certains groupes hyperboliques.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3030
Classification: 20F65, 20F67, 30L10
Mot clés : cohomologie $\ell _p$, dimension conforme, espaces hyperboliques
Keywords: $\ell _p$-cohomology, conformal dimension, hyperbolic spaces

Bourdon, Marc 1

1 Laboratoire Painlevé UMR CNRS 8524 Université de Lille 1 59655 Villeneuve d’Ascq (France) 
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Bourdon, Marc. Cohomologie $\ell _p$ en degrés supérieurs et dimension conforme. Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 1013-1043. doi : 10.5802/aif.3030. https://aif.centre-mersenne.org/articles/10.5802/aif.3030/

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