Topological property (T) for groupoids

Clément Dell'Aiera; Rufus Willett

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arXiv · 1811.07085

Topological property (T) for groupoids

Clément Dell'Aiera·Rufus Willett

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Abstract

We introduce a notion of topological property (T) for \'etale 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.

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BibTeX RIS

Clément Dell'Aiera, Rufus Willett. 2018-11-17. Topological property (T) for groupoids. https://arxiv.org/abs/1811.07085

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