Module derivations and cohomological splitting of adjoint bundles

• Autorzy: Akira Kono , Katsuhiko Kuribayashi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57T35: Applications of Eilenberg-Moore spectral sequences
• 55T20: Eilenberg-Moore spectral sequences
• 55S05: Primary cohomology operations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 180
• Numer: 3
• Strony: 199-221

Daty

wydano

2003

Twórcy

autor

Akira Kono

• Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan

autor

Katsuhiko Kuribayashi

• Department of Applied Mathematics, Faculty of Science, Okayama University of Science, Okayama 700-0005, Japan

Identyfikatory

DOI

10.4064/fm180-3-1