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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 17th 2012
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   Author: Urs
   Format: MarkdownItexbrief entry on _[[Turaev-Viro model]]_, an entry long overdue. But for the moment it just records some references. Bruce Bartlett has a comment on what is currently the last of these references and he will post it below in a moment...

   brief entry on Turaev-Viro model, an entry long overdue. But for the moment it just records some references.

   Bruce Bartlett has a comment on what is currently the last of these references and he will post it below in a moment…

2. • CommentRowNumber2.
   • CommentAuthorBruce Bartlett
   • CommentTimeOct 17th 2012
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   Author: Bruce Bartlett
   Format: HtmlThanks to the elegant Kirillov and Kirillov-Balsam papers, given a spherical category A, we now know of four ways of setting up the 3d TQFT vector space of a surface Sigma: 1. As the Reshetikhin-Turaev vector space, based on the modular category Z(A) : has basis given by loops labelled by the simple objects in Z(A) running around the holes in Sigma. 2. As the TV vector space: triangulate Sigma, and sum over all tensor products of labellings of the edges by simple objects in A. There is a canonical projector on this space; the image of this projector is the TV vector space. 3. As the Levin-Wen ground state space of a Hamiltonian operator operating on a triangulation of Sigma, based on the 6j symbols of A. 4. As the Kitaev-Kirillov-Levin-Wen string-net space of linear combinations of string diagrams drawn on Sigma up to local moves of string diagrams. The string-net space (number 4) is the most intriguing to me.

   Thanks to the elegant Kirillov and Kirillov-Balsam papers, given a spherical category A, we now know of four ways of setting up the 3d TQFT vector space of a surface Sigma:
   
   1. As the Reshetikhin-Turaev vector space, based on the modular category Z(A) : has basis given by loops labelled by the simple objects in Z(A) running around the holes in Sigma.
   
   2. As the TV vector space: triangulate Sigma, and sum over all tensor products of labellings of the edges by simple objects in A. There is a canonical projector on this space; the image of this projector is the TV vector space.
   
   3. As the Levin-Wen ground state space of a Hamiltonian operator operating on a triangulation of Sigma, based on the 6j symbols of A.
   
   4. As the Kitaev-Kirillov-Levin-Wen string-net space of linear combinations of string diagrams drawn on Sigma up to local moves of string diagrams.
   
   The string-net space (number 4) is the most intriguing to me.
3. • CommentRowNumber3.
   • CommentAuthorBruce Bartlett
   • CommentTimeOct 17th 2012
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   Author: Bruce Bartlett
   Format: HtmlFor instance, the string-net space seems to be an elegant alternative approach to the concept of "holonomy" of nonabelian gerbes. One might say that the holonomy -is- the string net space.

   For instance, the string-net space seems to be an elegant alternative approach to the concept of "holonomy" of nonabelian gerbes. One might say that the holonomy -is- the string net space.
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 18th 2014
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   Author: Urs
   Format: MarkdownItexhave added more references, with brief comments, to the entry _[[Turaev-Viro model]]_

   have added more references, with brief comments, to the entry Turaev-Viro model