Cohomologie ${\ell }_p$ en degrés supérieurs et dimension conforme

Bourdon, Marc

Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 1013-1043.

On donne une condition suffisante pour l’annulation de la cohomologie ${\ell }_p$ 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.

We establish a sufficient condition for vanishing of the ${\ell }_p$-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.

Classification : 20F65, 20F67, 30L10
Mot clés : cohomologie $\ell _p$, dimension conforme, espaces hyperboliques
Keywords: $\ell _p$-cohomology, conformal dimension, hyperbolic spaces

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