We investigate if, for a locally compact group G, the Fourier algebra A(G) is biflat in the sense of quantized Banach homology. A central rôle 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 × 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 × G fails to have an approximate indicator.
We characterize open embeddings of Stein spaces and of C ∞ -manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras.
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