A-T-menability and metric amenability for HLS groupoids

@misc{qiao2026atmenability,
  title = {{A-T-menability and metric amenability for HLS groupoids}},
  author = {Yu Qiao and Hao Song and Yan Wang and Jiawen Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39479},
  eprint = {2610.39479},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39479},
  note = {CC0},
}

TY  - UNPB
TI  - A-T-menability and metric amenability for HLS groupoids
AU  - Yu Qiao
AU  - Hao Song
AU  - Yan Wang
AU  - Jiawen Zhang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39479
UR  - https://arxiv.org/abs/2610.39479
AB  - 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 𝔽_2. The two separating examples are constructed using relative expansion and twisted spectral-gap techniques, respectively.
ER  -