Cocycle Constructions for Topological Field Theories

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Lipsky, David

Contributors dc:contributor

• Ando, Matthew
• McCarthy, Randy
• Rezk, Charles
• Guillou, Bertrand

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

Statement dc:rights

• Copyright 2010 David Lipsky

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16929

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16929