The Furstenberg Boundary of a Groupoid

Clemens Borys

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arXiv · 1904.10062

The Furstenberg Boundary of a Groupoid

Clemens Borys

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Abstract

We define the Furstenberg boundary of a locally compact Hausdorff \'etale 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 \'etale groupoid with compact unit space and no fixed points. This yields a criterion for C*-simplicity of minimal groupoids.

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Clemens Borys. 2019-04-22. The Furstenberg Boundary of a Groupoid. https://arxiv.org/abs/1904.10062

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