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Module derivations and cohomological splitting of adjoint bundles

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Kono A., Kuribayashi K.

Fundamenta Mathematicae

2003

tom 180

nr 3

199-221

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 operations in general. As a consequence, we can show that the isomorphism class of an SU(n)-adjoint bundle over a 4-dimensional CW complex coincides with the homotopy equivalence class of the bundle.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Kono A.

1 Kuribayashi K.

1 2003

Wyniki wyszukiwania

Module derivations and cohomological splitting of adjoint bundles