Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 1, Number 2 (2001), 743-762.
Splitting of Gysin extensions
Let be an orientable sphere bundle. Its Gysin sequence exhibits as an extension of –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 corresponding to a component of its –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 is a formal space; the second, with integer coefficients, is where is a torus.
Algebr. Geom. Topol., Volume 1, Number 2 (2001), 743-762.
Received: 11 October 2000
Revised: 17 July 2001
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 16E45: Differential graded algebras and applications 55R25: Sphere bundles and vector bundles 55S35: Obstruction theory
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 55R20: Spectral sequences and homology of fiber spaces [See also 55Txx] 55S20: Secondary and higher cohomology operations 55S30: Massey products
Berrick, A J; Davydov, A A. Splitting of Gysin extensions. Algebr. Geom. Topol. 1 (2001), no. 2, 743--762. doi:10.2140/agt.2001.1.743. https://projecteuclid.org/euclid.agt/1513882647