The Cohomology of Classifying Spaces of H-spaces

Let G denote an associative iï-space with unit (e.g. a topological group). We will show that the relations between G and a classifying space B Q axe more readily displayed using a geometric analog of the resolutions of homological algebra. The analogy is quite sharp, the stages of the resolution, whose base is BQ, determine a filtration of BQ. The resulting spectral sequence for cohomology is independent of the choice of the resolution, it converges to H*(BQ), and its JE2term is ExtH(0)(R, R) (i? = ground ring). We thus obtain spectral sequences of the Eilenberg-Moore type [5] in a simpler and more geometric manner.