{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/126922"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/126922","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"An Orientation map for height p - 1 real E theory","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Chatham, Hood,IV(Robert Hood)"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Haynes Miller."],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-22T22:21:04Z","subjects":["Mathematics."],"languages":["eng"],"rights":["MIT theses may be protected by copyright. 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Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1721.1/126922"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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)."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["An Orientation map for height p - 1 real E theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Haynes Miller."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics","Math"],"dc:contributor.other":["Massachusetts Institute of Technology. Department of Mathematics."],"dc:creator":["Chatham, Hood,IV(Robert Hood)"],"dc:date.accessioned":["2020-09-03T16:40:41Z"],"dc:date.available":["2020-09-03T16:40:41Z"],"dc:date.issued":["2020"],"dc: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)."],"dc:description.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."],"dc:description.degree":["Ph. D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/126922"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["MIT theses may be protected by copyright. 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