Cocycle Constructions for Topological Field Theories

Lipsky, David

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

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

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

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

Copyright and License Information

Copyright 2010 David Lipsky

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