The Furstenberg Boundary of a Groupoid

Abstract

We define the Furstenberg boundary of a locally compact Hausdorff étale groupoid, generalising the Furstenberg boundary for discrete groups, by providing a construction of a groupoid-equivariant injective envelope. Using this injective envelope, we establish the absence of recurrent amenable subgroups in the isotropy as a sufficient criterion for the intersection property of a locally compact Hausdorff étale groupoid with compact unit space and no fixed points. This yields a criterion for C*-simplicity of minimal groupoids.

arXiv comment20 pages, last section on applications to C*-simplicity added to previous version

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Cited by in corpus (1)

• The ideal intersection property for essential groupoid C*-algebras