Topological equivalences for differential graded algebras
Algebraic Topology
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/0604259,
title = {Topological equivalences for differential graded algebras},
author = {Daniel Dugger and Brooke Shipley},
journal= {arXiv preprint arXiv:math/0604259},
year = {2007}
}
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