  Let X --> B be an orientable sphere bundle. Its Gysin sequence exhibits
H^*(X) as an extension of H^*(B)-modules. We prove that the class of this
extension is the image of a canonical class that we define in the Hochschild
3-cohomology of H^*(B), corresponding to a component of its A_infty-structure,
and generalizing the Massey triple product. We identify two cases where this
class vanishes, so that the Gysin extension is split. The first, with rational
coefficients, is that where B is a formal space; the second, with integer
coefficients, is where B is a torus.
