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Massey products and uniqueness of \(A_\infty\) algebra structures Muro, Fernando


Classical obstructions to the existence and uniqueness of \(A\)-infinity algebra structures on spectra live in the Hochschild cohomology of the stable homotopy ring. Hence, classical existence and uniqueness results rely on the vanishing of this cohomology. Angeltveit considered finer obstructions in the pages of a spectral sequence computing the homotopy groups of the moduli space of \(A\)-infinity algebra structures. We calculate the second differential of this spectral sequence in terms of Massey products. As an application, we obtain existence and uniqueness results even when the Hochschild cohomology algebra is highly non-trivial.

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