The authors resolve the p=1 case of Thom's question by establishing the existence of groups that are not L^1-approximable.
Eckhardt, Residually finite amenable groups that are not Hilbert-Schmidt stable, arXiv preprint arXiv:2501.07791 (2025)
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On $L^1$-approximation of groups
The authors resolve the p=1 case of Thom's question by establishing the existence of groups that are not L^1-approximable.