2008/01/10 by Frankild, Anders J., Jorgensen, Peter · 2 citations
#16E45 (Primary) 55P62 (Secondary) #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0801.1581
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.