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You searched for subject:(Dyer Lashof operations). Showing records 1 – 2 of 2 total matches.

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University of Illinois – Chicago

1. Bayindir, Haldun Ozgur. Topological Equivalences of E-infinity Differential Graded Algebras.

Degree: 2018, University of Illinois – Chicago

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. Advisors/Committee Members: Shipley, Brooke (advisor), Bousfield, Aldridge K (committee member), Antieau, Benjamin (committee member), Gillet, Henri (committee member), Mathew, Akhil (committee member), Shipley, Brooke (chair).

Subjects/Keywords: Dyer-Lashof operations; Differential graded algebras; Commutative ring spectra; Obstruction theory

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APA (6th Edition):

Bayindir, H. O. (2018). Topological Equivalences of E-infinity Differential Graded Algebras. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/23145

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Bayindir, Haldun Ozgur. “Topological Equivalences of E-infinity Differential Graded Algebras.” 2018. Thesis, University of Illinois – Chicago. Accessed July 15, 2020. http://hdl.handle.net/10027/23145.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Bayindir, Haldun Ozgur. “Topological Equivalences of E-infinity Differential Graded Algebras.” 2018. Web. 15 Jul 2020.

Vancouver:

Bayindir HO. Topological Equivalences of E-infinity Differential Graded Algebras. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/10027/23145.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bayindir HO. Topological Equivalences of E-infinity Differential Graded Algebras. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/23145

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Wayne State University

2. Tilson, Sean Michael. Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications.

Degree: PhD, Mathematics, 2013, Wayne State University

We construct Power operations in the K"unneth spectral sequence and the C2 equivariant Adams spectral sequence. While the operations in the K"unneth spectral sequence are 0 in Tor, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having Einfty ring maps. The operations in the C2-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory. Advisors/Committee Members: Robert R. Bruner.

Subjects/Keywords: Dyer-Lashof; power operations; ring spectra; spectral sequence; stable homotopy; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Tilson, S. M. (2013). Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications. (Doctoral Dissertation). Wayne State University. Retrieved from https://digitalcommons.wayne.edu/oa_dissertations/800

Chicago Manual of Style (16th Edition):

Tilson, Sean Michael. “Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications.” 2013. Doctoral Dissertation, Wayne State University. Accessed July 15, 2020. https://digitalcommons.wayne.edu/oa_dissertations/800.

MLA Handbook (7th Edition):

Tilson, Sean Michael. “Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications.” 2013. Web. 15 Jul 2020.

Vancouver:

Tilson SM. Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications. [Internet] [Doctoral dissertation]. Wayne State University; 2013. [cited 2020 Jul 15]. Available from: https://digitalcommons.wayne.edu/oa_dissertations/800.

Council of Science Editors:

Tilson SM. Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications. [Doctoral Dissertation]. Wayne State University; 2013. Available from: https://digitalcommons.wayne.edu/oa_dissertations/800

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