No quasi-isomorphism between a minimal Sullivan algebra of non-finite type and its realization

Abstract

We prove that the morphisms from a minimal Sullivan algebra of non-finite type to the algebra of polynomial differential forms on its realization cannot be quasi-isomorphic. This provides a positive answer to a question posed by F\'elix, Halperin and Thomas. Furthermore, we give some discussion about the relationship between the homotopy groups of a topological space and its minimal Sullivan model.