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    Turaev-Viro theory as an extended TQFT

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    Balsam_grad.sunysb_0771E_11015.pdf (1.237Mb)
    Date
    1-Aug-12
    Author
    Balsam, Benjamin
    Publisher
    The Graduate School, Stony Brook University: Stony Brook, NY.
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    Abstract
    In recent years, the application of quantum groups to the study of low-dimensional topology has become an active topic of research. In three-dimensions, these yield the well-known Reshetihkin-Turaev (RT) invariants, which are a mathematical formulation of Chern- Simons theory and Turaev-Viro (TV) theory, which is a convergent form of the Ponzano-Regge state sum formula from Quantum Gravity. Both RT and TV are more than invariants;they have a far richer structure known as a Topological Quantum Field Theory (TQFT). We describe Turaev-Viro theory as an extended (3-2-1)-TQFT and use this description to prove a theorem relating it to RT theory. Turaev-Viro theory has several equivalent descriptions. We examine Kitaev's toric code from quantum computation and the Levin- Wen model from condensed matter physics and show that these theories are extended TQFTs coinciding with TV theory.
    Description
    192 pg.
    URI
    http://hdl.handle.net/1951/59574
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    • Stony Brook Theses & Dissertations [SBU] [1955]

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