Topological equivalences for differential graded algebras

• Autores: Daniel Dugger, Brooke Shipley
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 1, 2007, págs. 37-61
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.09.013
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• Resumen

  • 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 counterexamples of the converse. We also develop an associated notion of topological Morita equivalence using a homotopical version of tilting.