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Download fileTopological Equivalences of E-infinity Differential Graded Algebras
thesis
posted on 2018-11-28, 00:00 authored by Haldun Ozgur BayindirTwo 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, BrookeChair
Shipley, BrookeDepartment
Mathematics, Statistics, and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral