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2018 Topological equivalences of E-infinity differential graded algebras
Haldun Özgür Bayındır
Algebr. Geom. Topol. 18(2): 1115-1146 (2018). DOI: 10.2140/agt.2018.18.1115

Abstract

Two DGAs are said to be topologically equivalent when the corresponding Eilenberg–Mac Lane ring spectra are weakly equivalent as ring spectra. Quasi-isomorphic DGAs are topologically equivalent, but the converse is not necessarily true. As a counterexample, Dugger and Shipley showed that there are DGAs that are nontrivially topologically equivalent, ie topologically equivalent but not quasi-isomorphic.

In this work, we define E topological equivalences and utilize the obstruction theories developed by Goerss, Hopkins and Miller to construct first examples of nontrivially E topologically equivalent E DGAs. Also, we show using these obstruction theories that for coconnective E F p –DGAs, E topological equivalences and quasi-isomorphisms agree. For E F p –DGAs with trivial first homology, we show that an E topological equivalence induces an isomorphism in homology that preserves the Dyer–Lashof operations and therefore induces an H F p –equivalence.

Citation

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Haldun Özgür Bayındır. "Topological equivalences of E-infinity differential graded algebras." Algebr. Geom. Topol. 18 (2) 1115 - 1146, 2018. https://doi.org/10.2140/agt.2018.18.1115

Information

Received: 22 May 2017; Revised: 18 October 2017; Accepted: 27 October 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859616
MathSciNet: MR3773750
Digital Object Identifier: 10.2140/agt.2018.18.1115

Subjects:
Primary: 18G55, 55P43, 55S12, 55S35, 55U99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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