English

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.

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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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R2 v1 2026-07-22T17:34:23.263Z