Cohomology rings of multiplicative fibrations

The coalgebra structure of the cohomology of multiplicative fibrations

“…The proof of the Main Theorem relies on a Borel decomposition [4] of H * ( X; Z p ) that arises from analyzing the Serre spectral sequence of the fibration ΩK − → j X − → ρ X. In this spectral sequence there are algebra isomorphisms…”

“…Many of these Postnikov systems are constructed in Section 3 of [4]. The images of these liftings applied to universal elements of the Postnikov systems are representatives of the generators of H * ( X; Z p ).…”

“…We will repeatedly refer to the notation of [4] because all generators of H * ( X; Z p ) are described by that paper. All homologies and cohomologies will have coefficients in Z p , the integers mod p for p an odd prime.…”

“…Let E 8 be the simple simply connected compact exceptional Lie group of type E 8 . In [4] we computed the mod 3 cohomology of the 3-connective cover of E 8 .…”

“…By the Main Theorem of [4], if E 8 is the 3-connective cover of E 8 , there is an algebra isomorphism…”