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Cocycle Constructions for Topological Field Theories

Author: David Lipsky; Matthew Ando; Randy McCarthy; Charles Rezk; Bertrand Guillou
Publisher: Urbana, IL.: University of Illinois, 2010.
Dissertation: Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2010.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : Manuscript : eBook   Computer File   Archival Material : English
Database:WorldCat
Summary:
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  Read more...
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Details

Material Type: Document, Thesis/dissertation, Manuscript, Internet resource
Document Type: Internet Resource, Computer File, Archival Material
All Authors / Contributors: David Lipsky; Matthew Ando; Randy McCarthy; Charles Rezk; Bertrand Guillou
OCLC Number: 776215812
Notes: Vita.
Description: 1 pdf file.
Details: System requirement: Adobe Acrobat Reader.; Mode of access: World Wide Web.
Responsibility: by David Lipsky.

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.

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