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I am interested in topological quantum field theory (TQFT). It seems that there are many types of TQFTs. The first book I pick up is "Quantum invariants of knots and 3-manifolds" by Turaev. But it doesn't say which type of TQFT are dealt in the book. I found at least two TQFTs which contain Turaev's name, namely Turaev-Viro and Turaev-Reshetikhin TQFT. I have searched the definitions of various TQFTs for few days but I couldn't find good resources.

I would like to know

  1. which type of TQFT is dealt in Turaev's book.
  2. good resources for definitions of various TQFTs (or if it is not difficult to answer here, please give me definitions.)
  3. whether they are esentially different objects or some are generalizations of the others.
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How much of Touraev's "Quantum invariants of knots and 3-manifolds" did you read? Chapter III is TQFT axiomatics, so you it's probably relevant to any TQFT you run into. –  Neal Apr 14 '12 at 1:44
    
You should also search mathoverflow. TQFTs are sexy right now, so there are plenty of questions dealing with them -- e.g., mathoverflow.net/questions/386/…, mathoverflow.net/questions/27574/…, mathoverflow.net/questions/4813/turaev-viro-extended-tqft, etc. There was also a presentation on Lurie's work on TQFTs at the Joint Meetings this January that might be a useful survey for you if you can get your hands on the paper. –  Neal Apr 14 '12 at 1:50

1 Answer 1

up vote 2 down vote accepted

Review of a recent Turaev book at http://www.ams.org/journals/bull/2012-49-02/S0273-0979-2011-01351-9/ also discussing earlier volumes to some extent.

Here we go, the book you ask about: http://www.ams.org/journals/bull/1996-33-01/S0273-0979-96-00621-0/home.html

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Note that there is a revised edition of "Quantum invariants of knots and 3-manifolds" published in 2010. According to the foreword, the problem list was deleted, some errors were corrected, and the bibliography was updated. –  Neal Apr 14 '12 at 2:14
    
@Neal, understood. I do not expect there would be a separate book review in the Bulletin, but I will check. It depends on whether the new edition discusses significant progress in the subject area. –  Will Jagy Apr 14 '12 at 2:34
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I don't think it does; the foreword specifically notes that the author's comments in the chapters still reflect the field as of 1994. –  Neal Apr 14 '12 at 21:26

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