Homological properties of cochain Differential Graded algebras

Details Homological properties of cochain Differential Graded algebras Homological properties of cochain Differential Graded algebras

2008-01-10

arxiv.org/abs/0801.1581v1

Mathematics

Rings and Algebras

21 pages

Scientific paper

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.

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