University of Illinois Urbana-Champaign

Cocycle Constructions for Topological Field Theories

Lipsky, David

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Lipsky_David.pdf

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

Description

Title
Cocycle Constructions for Topological Field Theories
Author(s)
Lipsky, David
Issue Date
2010-08-20T18:02:12Z
Director of Research (if dissertation) or Advisor (if thesis)
Ando, Matthew
Doctoral Committee Chair(s)
McCarthy, Randy
Committee Member(s)
  • Ando, Matthew
  • Rezk, Charles
  • Guillou, Bertrand
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2010-08-20T18:02:12Z
Keyword(s)
  • Algebraic topology
  • Topological field theory
  • Smooth Deligne cohomology
  • Cech cohomology
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.
Graduation Semester
2010-08
Permalink
http://hdl.handle.net/2142/16929
Copyright and License Information
Copyright 2010 David Lipsky

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