{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16929"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16929","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Cocycle Constructions for Topological Field Theories","abstract":"In this thesis, we explore a chain-level construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds $\\Sigma$, this construction takes the form of a chain map $\\tau_\\Sigma$ from the smooth \\v{C}ech-Deligne complex on a manifold $X$ to a degree-shifted version of the same complex on the mapping space $X^\\Sigma$. More generally, if $\\Sigma$ has boundary $\\partial \\Sigma$, the construction produces a chain null-homotopy of the chain map $\\tau_{\\partial \\Sigma}$ associated to the boundary.","abstract_html":"In this thesis, we explore a chain-level construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds $\\Sigma$, this construction takes the form of a chain map <span class=\"etd-inline-math\">\\tau<sub>\\</sub>Sigma</span> from the smooth \\v{C}ech-Deligne complex on a manifold $X$ to a degree-shifted version of the same complex on the mapping space <span class=\"etd-inline-math\">X<sup>\\</sup>Sigma</span>. More generally, if $\\Sigma$ has boundary $\\partial \\Sigma$, the construction produces a chain null-homotopy of the chain map <span class=\"etd-inline-math\">\\tau<sub>\\partial \\Sigma</sub></span> associated to the boundary.","abstract_has_math":true,"creators":["Lipsky, David"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ando, Matthew","McCarthy, Randy","Rezk, Charles","Guillou, Bertrand"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-20T18:02:12Z","date_published":"2010-08-20T18:02:12Z","updated_at":"2026-07-22T22:25:09Z","subjects":["Algebraic topology","Topological field theory","Smooth Deligne cohomology","Cech cohomology"],"languages":["en"],"rights":["Copyright 2010 David Lipsky"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16929","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ando, Matthew","McCarthy, Randy","Rezk, Charles","Guillou, Bertrand"]},{"key":"dc:creator","label":"Author","values":["Lipsky, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-08-20T18:02:12Z","2010-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic topology","Topological field theory","Smooth Deligne cohomology","Cech cohomology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 David Lipsky"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/16929"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we explore a chain-level construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds $\\Sigma$, this construction takes the form of a chain map $\\tau_\\Sigma$ from the smooth \\v{C}ech-Deligne complex on a manifold $X$ to a degree-shifted version of the same complex on the mapping space $X^\\Sigma$. More generally, if $\\Sigma$ has boundary $\\partial \\Sigma$, the construction produces a chain null-homotopy of the chain map $\\tau_{\\partial \\Sigma}$ associated to the boundary.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-15T21:35:23Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Lipsky_David.pdf: 377940 bytes, checksum: fb426bac4adde85e62e64fe2d27c5031 (MD5)","Made available in DSpace on 2010-08-20T18:02:12Z (GMT). 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More generally, if $\\Sigma$ has boundary $\\partial \\Sigma$, the construction produces a chain null-homotopy of the chain map $\\tau_{\\partial \\Sigma}$ associated to the boundary.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-15T21:35:23Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Lipsky_David.pdf: 377940 bytes, checksum: fb426bac4adde85e62e64fe2d27c5031 (MD5)","Made available in DSpace on 2010-08-20T18:02:12Z (GMT). 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