Bockstein closed 2-group extensions and cohomology of quadratic maps
نویسندگان
چکیده
منابع مشابه
Bockstein Closed 2-Group Extensions and Cohomology of Quadratic Maps
A central extension of the form E : 0 → V → G → W → 0, where V and W are elementary abelian 2-groups, is called Bockstein closed if the components qi ∈ H ∗(W,F2) of the extension class of E generate an ideal which is closed under the Bockstein operator. In this paper, we study the cohomology ring of G when E is a Bockstein closed 2-power exact extension. The mod-2 cohomology ring of G has a sim...
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Let E be a central extension of the form 0 → V → G → W → 0 where V and W are elementary abelian 2-groups. Associated to E there is a quadratic map Q : W → V given by the 2-power map which uniquely determines the extension. This quadratic map also determines the extension class q of the extension in H(W,V ) and an ideal I(q) in H(G,Z/2) which is generated by the components of q. We say E is Bock...
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There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in the r-th page of the spectral sequence provided differentials di = 0 for all i < r. If L further decomposes into a sum of G-sublattice L = L ⊕ L, we show tha...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.01.029