2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145698Consider 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.21 pagesRings and AlgebrasK-Theory and Homology16E45 (Primary) 55P62 (Secondary)text