2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63674We investigate if, for a locally compact group $G$, the Fourier algebra $A(G)$ is biflat in the sense of quantized Banach homology. A central role in our investigation is played by the notion of an approximate indicator of a closed subgroup of $G$: The Fourier algebra is operator biflat whenever the diagonal in $G \times G$ has an approximate indicator. Although we have been unable to settle the question of whether $A(G)$ is always operator biflat, we show that, for $G = SL(3,C)$, the diagonal in $G \times G$ fails to have an approximate indicator.23 pages; more typos removed; references updatedFunctional AnalysisK-Theory and HomologyOperator Algebras22D25 (primary), 22E10, 43A30, 46L07, 46L89, 46M18, 47L25, 47L50text