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Bi-exact Wreath-like Product Groups

  • Ionuţ Chifan
  • Zhiyuan Yang
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Abstract

In this short paper, we prove the bi-exactness of all wreath-like product groups G∈𝒲ℛ(A,Bcurvearrowright I), whenever A is amenable, B is bi-exact, and the action Bcurvearrowright I has amenable stabilizers. As applications, we obtain solidity for the associated group von Neumann algebras and, by combining our result with existing rigidity theorems, new examples exhibiting the McDuff superrigidity.

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Cite

BibTeXRIS
BibTeX
@misc{chifan2026biexact,
  title = {{Bi-exact Wreath-like Product Groups}},
  author = {Ionuţ Chifan and Zhiyuan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24923},
  eprint = {2609.24923},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24923},
}
RIS
TY  - UNPB
TI  - Bi-exact Wreath-like Product Groups
AU  - Ionuţ Chifan
AU  - Zhiyuan Yang
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24923
UR  - https://arxiv.org/abs/2609.24923
AB  - In this short paper, we prove the bi-exactness of all wreath-like product groups G∈𝒲ℛ(A,Bcurvearrowright I), whenever A is amenable, B is bi-exact, and the action Bcurvearrowright I has amenable stabilizers. As applications, we obtain solidity for the associated group von Neumann algebras and, by combining our result with existing rigidity theorems, new examples exhibiting the McDuff superrigidity.
ER  -