Browsing by Subject "Group extensions"

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    Bockstein closed 2-group extensions and cohomology of quadratic maps
    (Elsevier, 2012-05-01) Pakianathan, J.; Yalçın, E.
    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,F 2) 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 simple form and it is easy to calculate. The main result of the paper is the calculation of the Bocksteins of the generators of the mod-2 cohomology ring using an Eilenberg-Moore spectral sequence. We also find an interpretation of the second page of the Bockstein spectral sequence in terms of a new cohomology theory that we define for Bockstein closed quadratic maps Q:. W→ V associated to the extensions E of the above form. © 2012 Elsevier Inc.
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    Free actions of p-groups on products of lens spaces
    (American Mathematical Society, 2000-09-20) Yalçın, E.
    Let p be an odd prime number. We prove that if (Z=p)r acts freely on a product of k equidimensional lens spaces, then r k. This settles a special case of a conjecture due to C. Allday. We also nd further restrictions on non-abelian p-groups acting freely on a product of lens spaces. For actions inducing a trivial action on homology, we reach the following characterization: A p-group can act freely on a product of k lens spaces with a trivial action on homology if and only if rk(G) k and G has the -extension property. The main technique is to study group extensions associated to free actions.