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2001 Splitting of Gysin extensions
A J Berrick, A A Davydov
Algebr. Geom. Topol. 1(2): 743-762 (2001). DOI: 10.2140/agt.2001.1.743

Abstract

Let XB 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.

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A J Berrick. A A Davydov. "Splitting of Gysin extensions." Algebr. Geom. Topol. 1 (2) 743 - 762, 2001. https://doi.org/10.2140/agt.2001.1.743

Information

Received: 11 October 2000; Revised: 17 July 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0986.55014
MathSciNet: MR1875616
Digital Object Identifier: 10.2140/agt.2001.1.743

Subjects:
Primary: 16E45, 55R25, 55S35
Secondary: 16E40, 55R20, 55S20, 55S30

Rights: Copyright © 2001 Mathematical Sciences Publishers

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