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Topological Property (T) for groupoids

Topological Property (T) for groupoids

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 …