We establish a sufficient condition for vanishing of the -cohomology of hyperbolic uniformly contractible simplicial complexes, in degree at least . 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 en degré supérieur à , 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.
Revised:
Accepted:
Published online:
Classification: 20F65, 20F67, 30L10
Keywords: -cohomology, conformal dimension, hyperbolic spaces
@article{AIF_2016__66_3_1013_0, author = {Bourdon, Marc}, title = {Cohomologie $\ell _p$ en degr\'es sup\'erieurs et dimension conforme}, journal = {Annales de l'Institut Fourier}, pages = {1013--1043}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {66}, number = {3}, year = {2016}, doi = {10.5802/aif.3030}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3030/} }
TY - JOUR TI - Cohomologie $\ell _p$ en degrés supérieurs et dimension conforme JO - Annales de l'Institut Fourier PY - 2016 DA - 2016/// SP - 1013 EP - 1043 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3030/ UR - https://doi.org/10.5802/aif.3030 DO - 10.5802/aif.3030 LA - fr ID - AIF_2016__66_3_1013_0 ER -
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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