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 Title: Cocycle Constructions for Topological Field Theories Author(s): Lipsky, David Director of Research: Ando, Matthew Doctoral Committee Chair(s): McCarthy, Randy Doctoral Committee Member(s): Ando, Matthew; Rezk, Charles; Guillou, Bertrand Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Algebraic topology Topological field theory Smooth Deligne cohomology Cech cohomology 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. Issue Date: 2010-08-20 URI: http://hdl.handle.net/2142/16929 Rights Information: Copyright 2010 David Lipsky Date Available in IDEALS: 2010-08-20 Date Deposited: 2010-08
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