[Propriété (T) topologique pour les groupoïdes]
Nous définissons une notion de propriété (T) pour les groupoïdes étales. Elle généralise à la fois la propriété (T) de Kazhdan pour les groupes, et la propriété (T) géométrique pour les espaces grossiers. Notre but principal est l’application de cette propriété (T) à l’existence de projecteurs de type Kazhdan dans les -algèbres réduites et maximales des groupoïdes, dont nous explorons les conséquences sur l’exactitude, l’exactitude en -théorie, et sur la validité de la conjecture de Baum–Connes. Nous étudions aussi divers exemples, et comparons cette notion à d’autres versions de la propriété (T) ainsi qu’à la a-T-moyennabilité.
We introduce a notion of topological Property (T) for étale groupoids. This simultaneously generalizes Kazhdan’s Property (T) for groups and geometric Property (T) for coarse spaces. One main goal is to use this Property (T) to prove the existence of so-called Kazhdan projections in both maximal and reduced groupoid -algebras, and explore applications of this to exactness, -exactness, and the Baum–Connes conjecture. We also study various examples, and discuss the relationship with other notions of Property (T) for groupoids and with a-T-menability.
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Keywords: Property (T), Topological groupoids, Coarse geometry, Expander
Mot clés : Propriété (T), groupoïdes topologiques, géométrie grossière, expanseurs
Dell’Aiera, Clément 1 ; Willett, Rufus 2
CC-BY-ND 4.0
@article{AIF_2022__72_3_1097_0,
author = {Dell{\textquoteright}Aiera, Cl\'ement and Willett, Rufus},
title = {Topological {Property~(T)} for groupoids},
journal = {Annales de l'Institut Fourier},
pages = {1097--1148},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {72},
number = {3},
year = {2022},
doi = {10.5802/aif.3513},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3513/}
}
TY - JOUR AU - Dell’Aiera, Clément AU - Willett, Rufus TI - Topological Property (T) for groupoids JO - Annales de l'Institut Fourier PY - 2022 SP - 1097 EP - 1148 VL - 72 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3513/ DO - 10.5802/aif.3513 LA - en ID - AIF_2022__72_3_1097_0 ER -
%0 Journal Article %A Dell’Aiera, Clément %A Willett, Rufus %T Topological Property (T) for groupoids %J Annales de l'Institut Fourier %D 2022 %P 1097-1148 %V 72 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3513/ %R 10.5802/aif.3513 %G en %F AIF_2022__72_3_1097_0
Dell’Aiera, Clément; Willett, Rufus. Topological Property (T) for groupoids. Annales de l'Institut Fourier, Tome 72 (2022) no. 3, pp. 1097-1148. doi : 10.5802/aif.3513. https://aif.centre-mersenne.org/articles/10.5802/aif.3513/
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