{"id":{"repo_id":"alabama","oai_identifier":"oai:ir.ua.edu:123456789/8204"},"canonical_url":"https://search.dev.ndltd.org/etd/alabama/oai:ir.ua.edu:123456789/8204","repository":{"repo_id":"alabama","name":"University of Alabama","base_url":"https://ir-api.ua.edu/oai/request"},"display":{"title":"A Classifying Family of Spaces for the Cohomology of Profinite Groups","abstract":"In 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.","abstract_html":"In 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.","abstract_has_math":false,"creators":["Lee, Evan Matthew"],"institution":"University of Alabama Libraries","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dixon, Martyn","Evans, Martin","Roberts, Lawrence","Tosun, Bulent","Harms, Benjamin"],"advisors":["Corson, Jon"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-27T18:44:23Z","subjects":["algebraic topology","classifying space","profinite groups","sheaf theory","topological algrebra"],"languages":["en_US","English"],"rights":["All rights reserved by the author unless otherwise indicated."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["http://purl.lib.ua.edu/181533","u0015_0000001_0003972","Lee_alatus_0004D_14522"],"render_values":[{"text":"http://purl.lib.ua.edu/181533","href":"http://purl.lib.ua.edu/181533","code":true},{"text":"u0015_0000001_0003972","href":null,"code":true},{"text":"Lee_alatus_0004D_14522","href":null,"code":true}]}]},"links":{"outbound_url":"http://ir.ua.edu/handle/123456789/8204","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dixon, Martyn","Evans, Martin","Roberts, Lawrence","Tosun, Bulent","Harms, Benjamin"]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Corson, Jon"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["University of Alabama Tuscaloosa"]},{"key":"dc:creator","label":"Author","values":["Lee, Evan Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-11-23T14:34:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-11-23T14:34:43Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:publisher","label":"Institution","values":["University of Alabama Libraries"]},{"key":"dc:type","label":"Dc Type","values":["thesis","text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["algebraic topology","classifying space","profinite groups","sheaf theory","topological algrebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["All rights reserved by the author unless otherwise indicated."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["http://purl.lib.ua.edu/181533","u0015_0000001_0003972","Lee_alatus_0004D_14522"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://ir.ua.edu/handle/123456789/8204"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Electronic Thesis or Dissertation"]},{"key":"dc:description.abstract","label":"Abstract","values":["In 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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["electronic"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A Classifying Family of Spaces for the Cohomology of Profinite Groups"]}]}],"canonical_facts":{"dc:contributor":["Dixon, Martyn","Evans, Martin","Roberts, Lawrence","Tosun, Bulent","Harms, Benjamin"],"dc:contributor.advisor":["Corson, Jon"],"dc:contributor.other":["University of Alabama Tuscaloosa"],"dc:creator":["Lee, Evan Matthew"],"dc:date.accessioned":["2021-11-23T14:34:43Z"],"dc:date.available":["2021-11-23T14:34:43Z"],"dc:date.issued":["2021"],"dc:description":["Electronic Thesis or Dissertation"],"dc:description.abstract":["In 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."],"dc:format.medium":["electronic"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["http://purl.lib.ua.edu/181533","u0015_0000001_0003972","Lee_alatus_0004D_14522"],"dc:identifier.uri":["http://ir.ua.edu/handle/123456789/8204"],"dc:language":["English"],"dc:language.iso":["en_US"],"dc:publisher":["University of Alabama Libraries"],"dc:rights":["All rights reserved by the author unless otherwise indicated."],"dc:subject":["algebraic topology","classifying space","profinite groups","sheaf theory","topological algrebra"],"dc:title":["A Classifying Family of Spaces for the Cohomology of Profinite Groups"],"dc:type":["thesis","text"]},"updated_at":"2026-07-27T18:44:23Z"}