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Ando, Matthew McCarthy, Randy Ando, Matthew Rezk, Charles Guillou, Bertrand Lipsky, David 2010-08-20T18:02:12Z 2010-08-20T18:02:12Z 2010-08-20T18:02:12Z 2010-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-15T21:35:23Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Lipsky_David.pdf: 377940 bytes, checksum: fb426bac4adde85e62e64fe2d27c5031 (MD5) Made available in DSpace on 2010-08-20T18:02:12Z (GMT). No. of bitstreams: 2 Lipsky_David.pdf: 377940 bytes, checksum: fb426bac4adde85e62e64fe2d27c5031 (MD5) license.txt: 4061 bytes, checksum: 404cde768576e29f9dbe71c6120c4625 (MD5) http://hdl.handle.net/2142/16929 en Copyright 2010 David Lipsky Algebraic topology Topological field theory Smooth Deligne cohomology Cech cohomology Cocycle Constructions for Topological Field Theories Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD