%0 Journal Article
%T Topological equivalences for differential graded algebras
%A Daniel Dugger
%A Brooke Shipley
%J Mathematics
%D 2006
%I arXiv
%X We investigate the relationship between differential graded algebras (dgas) and topological ring spectra. Every dga C gives rise to an Eilenberg-Mac Lane ring spectrum denoted HC. If HC and HD are weakly equivalent, then we say C and D are topologically equivalent. Quasi-isomorphic dgas are topologically equivalent, but we produce explicit counter-examples of the converse. We also develop an associated notion of topological Morita equivalence using a homotopical version of tilting.
%U http://arxiv.org/abs/math/0604259v2