Cocycle Constructions for Topological Field Theories

Algebraic topology;Topological field theory;Smooth Deligne cohomology;Cech cohomology

Lipsky, David

关键词: Algebraic topology;    Topological field theory;    Smooth Deligne cohomology;    Cech cohomology;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16929/Lipsky_David.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.