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arXiv · 2304.12262

Rapid Decay for Principal \'Etale Groupoids

Alex Weygandt
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Abstract

This work concerns a generalization of property (RD) from discrete groups to twisted \'etale groupoids equipped with a length function. We show that, under the assumption that the \'etale groupoid is principal, twisted property (RD) is equivalent to polynomial growth. This generalizes a result of Chen and Wei concerning rapid decay for metric spaces with bounded geometry. Additionally, some permanence properties of groupoid (RD) are established.

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Alex Weygandt. 2023-04-24. Rapid Decay for Principal \'Etale Groupoids. https://arxiv.org/abs/2304.12262

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