Homological properties of cochain Differential Graded algebras

Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group.In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality, an Auslander–Buchsbaum Equality, and a Gap Theorem. These were inspired by homological ring theory.By the so-called looking glass principle, one would expect that analogous results exist for simply connected cochain Differential Graded algebras, such as the singular cochain complex of a simply connected topological space.Indeed, this paper establishes such analogous results.