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http://worldcat.org/entity/work/id/1816656416

Cocycle Constructions for Topological Field Theories

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  • "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."

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  • "Cocycle Constructions for Topological Field Theories"

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