Splitting of Gysin extensions
نویسندگان
چکیده
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∞ -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. AMS Classification 16E45, 55R25, 55S35; 16E40, 55R20, 55S20, 55S30
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