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Thompson's group F is not weakly amenable
Abstract
Let F be Thompson's group, and let D be the set of dyadic rationals in [0,1]. We give an embedding of ℤ(D)rtimes F into F, where the semidirect product is defined by the natural action of F on D. Using this embedding, we deduce from the nonamenability of F that F is not weakly amenable.
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BibTeX
@misc{fujiwara2026thompsons,
title = {{Thompson's group $F$ is not weakly amenable}},
author = {Koji Fujiwara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27932},
eprint = {2610.27932},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27932},
}
RIS
TY - UNPB
TI - Thompson's group F is not weakly amenable
AU - Koji Fujiwara
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27932
UR - https://arxiv.org/abs/2610.27932
AB - Let F be Thompson's group, and let D be the set of dyadic rationals in [0,1]. We give an embedding of ℤ^(D)rtimes F into F, where the semidirect product is defined by the natural action of F on D. Using this embedding, we deduce from the nonamenability of F that F is not weakly amenable.
ER -