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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...

Truncated polynomial algebras over the Steenrod algebra.

Mohamed Ali (1990)

Publicacions Matemàtiques

It is shown that the classification of polynomial algebras over the mod p Steenrod algebra is an essentially different problem from the classification of polynomial algebras truncated at height greater than p over the Steenrod algebra.

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