Topological property (T) for groupoids

2018/11/17 by Clément Dell’Aiera, Dell'Aiera, Clément, Rufus Willett +1 · 1 citation
Mathematics · #22A22 #46L80 #46L85 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1811.07085

openalex publication_date 2018/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C^*-algebras, and explore applications of this to exactness, K-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.

Cited by

• Geometric property (T) for box spaces and sofic approximations

Related

• Cohomology of property T groupoids and applications
• Purely infinite locally compact Hausdorff étale groupoids and their C^*-algebras
• The ideal intersection property for essential groupoid C*-algebras
• Almost elementariness and fiberwise amenability for étale groupoids
• Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture