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We introduce a convolution on a 2-sphere and use it to show that the linearised Becchi-Rouet-Stora-Tyutin transformations and gauge fixing conditions of Einstein-Hilbert gravity coupled to a two-form and a scalar field, follow from the product of two Yang-Mills theories. This provides an example of the convolutive product of gauge theories on a nontrivial background. By introducing a time direction the product is shown to extend to the D = 1 + 2 Einstein-static universe.doi:10.1007/jhep06(2020)096 fatcat:bcn2bzbdsrfxnccq3vd35jvfd4