An Orientation map for height p - 1 real E theory
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1191254467-MIT.pdf
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487.91 KB
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Adobe PDF
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Author(s)
Chatham, Hood,IV(Robert Hood)
Advisor(s)
Haynes Miller.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
Let p be an odd prime and let EO = E[superscript hC] [subscript p-1] be the Cp αxed points of height p - 1 Morava E theory. We say that a spectrum X has algebraic EO theory if the splitting of K[subscript *](X) as an K[subscript *][Cp]-module lifts to a topological splitting of EO [subscript grave] X. We develop criteria to show that a spectrum has algebraic EO theory, in particular showing that any connective spectrum with mod p homology concentrated in degrees 2k(p - 1) has algebraic EO theory. As an application, we answer a question posed by Hovey and Ravenel [10] by producing a unital orientation MW [subscript 4p-4] --> EO analogous to the MSU orientation of KO at p = 2 where MW [subscript 4p-4] is the Thom spectrum of the (4p - 4)-connective Wilson space.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 43-44).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
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