An Orientation map for height p - 1 real E theory

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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Chatham, Hood,IV(Robert Hood)

Advisor dc:contributor.advisor

• Haynes Miller.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/126922

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/126922