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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
Degree Granting Institution:University of Illinois at Urbana-Champaign
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
Rights Information:Copyright 2010 David Lipsky
Date Available in IDEALS:2010-08-20
Date Deposited:2010-08

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