A Classifying Family of Spaces for the Cohomology of Profinite Groups

dc.contributorDixon, Martyn
dc.contributorEvans, Martin
dc.contributorRoberts, Lawrence
dc.contributorTosun, Bulent
dc.contributorHarms, Benjamin
dc.contributor.advisorCorson, Jon
dc.contributor.authorLee, Evan Matthew
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2021-11-23T14:34:43Z
dc.date.available2021-11-23T14:34:43Z
dc.date.issued2021
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractIn the study of homological algebra, one useful tool for studying the cohomology of a discrete group is that group's classifying space. In some sense, the classifying space captures both the group itself and a description of its cohomology for any action of the group on any coefficient module. While some constructions for a classifying space also apply to topological groups, the relationship of the resulting space to the group's cohomology is unclear. Profinite groups are a special case of topological groups, determined entirely as the limits of inverse systems of finite, discrete groups. The goal of this work is to construct for profinite groups as close an analog as possible to the classifying space of a discrete group. In particular, we are interested in the construction for a finite, discrete group's classifying space achieved by first producing the nerve of the group as a category and then taking its geometric realization to obtain a space with isomorphic cohomology groups. We proceed by extending each step of this process to apply to a profinite group using inverse limits, followed by correcting for a lack of continuity (in the sense of compatibility with inverse limits) in singular cohomology by applying alternative cohomology theories to the resulting sequence of spaces. The end result has a promising isomorphism to the cohomology of the group, with the possibility of a further isomorphism.en_US
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otherhttp://purl.lib.ua.edu/181533
dc.identifier.otheru0015_0000001_0003972
dc.identifier.otherLee_alatus_0004D_14522
dc.identifier.urihttp://ir.ua.edu/handle/123456789/8204
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectalgebraic topology
dc.subjectclassifying space
dc.subjectprofinite groups
dc.subjectsheaf theory
dc.subjecttopological algrebra
dc.titleA Classifying Family of Spaces for the Cohomology of Profinite Groupsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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