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Topological Equivalences of E-infinity Differential Graded Algebras

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posted on 28.11.2018, 00:00 authored by Haldun Ozgur Bayindir
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-infinity topological equivalences and utilize the obstruction theories developed by Goerss, Hopkins and Miller to construct first examples of nontrivially E-infinity topologically equivalent E-infinity DGAs. Also, we show using these obstruction theories that for coconnective E-infinity Fp–DGAs, E-infinity topological equivalences and quasi-isomorphisms agree. For E-infinity Fp–DGAs with trivial first homology, we show that an E-infinity topological equivalence induces an isomorphism in homology that preserves the Dyer–Lashof operations and therefore induces an H-infinity Fp–equivalence.

History

Advisor

Shipley, Brooke

Chair

Shipley, Brooke

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Bousfield, Aldridge K Antieau, Benjamin Gillet, Henri Mathew, Akhil

Submitted date

August 2018

Issue date

18/06/2018

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