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
more » ... ible 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. 2000 Mathematics Subject Classification: 55T20, 57T35, 55S05.
doi:10.4064/fm180-3-1 fatcat:xbg46txgwbghzkwtnusvc32npm