Abstract
We show that the biflatness—in the sense of A. Ya. Helemskiĭ—of the Fourier algebra A(G) of a locally compact group G forces G to either have an abelian subgroup of finite index or to be non-amenable without containing \({\mathbb{F}}_{2}\) as a closed subgroup. An analogous dichotomy is obtained for biprojectivity.
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