Topological equivalences for differential graded algebras
Daniel Dugger, Brooke Shipley
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.
Create a lesson
Related papers
The p-local topologoical period-index problem in dimensions 2p+2 and below
Diarmuid Crowley, Xing Gu
Toward Quillen stratification for the odd primary Steenrod algebra
John H. Palmieri
Indecomposable Uniform Families on the Adams 4-Line
Jordan Benson, Runji Li
Sn-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products
Mohammadali Aligholi
Cohomology of regular spherical actions
José Ignacio Royo Prieto, Martintxo Saralegi-Aranguren, Robert Wolak
Unfolding of symmetric monoidal (∞,n)-categories
Rune Haugseng, Thomas Nikolaus