Algebraic and geometric models for 𝐻₀-spaces

Abstract

For every H 0 {H_0} -space (i.e. a space whose rationalization is an H H -space) we construct a space J J depending only on H ∗ ( X ; Z ) {H^\ast }(X;{\mathbf {Z}}) and a rational homotopy equivalence J → X J \to X (i.e. J J is a universal space to the left of all H 0 {H_0} -spaces having the same integral cohomology ring as X X is constructed generalizing the James reduced product. We study also the integral cohomology of H 0 {H_0} -spaces and we prove that under certain conditions it contains an algebra with divided powers.