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arXiv · 2610.39479

A-T-menability and metric amenability for HLS groupoids

Yu Qiao·Hao Song·Yan Wang·Jiawen Zhang
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Abstract

We characterise coarse embeddability of box spaces into Hilbert space in terms of a-T-menability of the associated Higson-Lafforgue-Skandalis (HLS) groupoids. Moreover, we prove that a-T-menability and metric amenability are independent for HLS groupoids: all four possible combinations occur among HLS groupoids associated with approximating sequences of the free group $\mathbb F_2$. The two separating examples are constructed using relative expansion and twisted spectral-gap techniques, respectively.

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Yu Qiao, Hao Song, Yan Wang, Jiawen Zhang. 2026-10-29. A-T-menability and metric amenability for HLS groupoids. https://arxiv.org/abs/2610.39479

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