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Module derivations and cohomological splitting of adjoint bundles

Akira Kono, Katsuhiko Kuribayashi (2003)

Fundamenta Mathematicae

Let G be a finite loop space such that the mod p cohomology of the classifying space BG is a polynomial algebra. We consider when the adjoint bundle associated with a G-bundle over M splits on mod p cohomology as an algebra. In the case p = 2, an obstruction for the adjoint bundle to admit such a splitting is found in the Hochschild homology concerning the mod 2 cohomologies of BG and M via a module derivation. Moreover the derivation tells us that the splitting is not compatible with the Steenrod...

Un 3-polyGEM de cohomologie modulo 2 nilpotente

Donghua Jiang (2004)

Annales de l’institut Fourier

On construit un contre-exemple de la conjecture suivante : si la cohomologie modulo 2 réduite d'un polyGEM 1-connexe quelconque est de type fini et si elle n'est pas réduite à (0), alors elle contient au moins un élément non nilpotent.

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