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Hi I am looking for any papers which extends the Turaev-Viro TQFT to a 3-2-1 theory (i.e. allows manifolds with corners) . I know this construction is known, but I cannot find a source. Please help.

Thanks, Ben

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    $\begingroup$ Please, enter your name in your profile instead of signing your posts... $\endgroup$
    – Ben Webster ♦
    Commented Nov 10, 2009 at 5:02
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    $\begingroup$ Ben, I don't know the answer to your question yet, but I am going to the ams sectional meeting in St. Paul, where I am looking forward to hearing the answer in the talk: Turaev-Viro Invariants as an Extended TQFT. Alexander Kirillov, Jr, Stony Brook University Benjamin Balsam*, Stony Brook University (1058-81-254) :) $\endgroup$
    – Charlie Frohman
    Commented Mar 7, 2010 at 19:49

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As Charlie pointed out in comments Balsam and Kirillov were working on this, and since his comment they posted a preprint to the arxiv: http://arxiv.org/abs/1004.1533

For another point of view see Kevin Walker's notes in progress at http://canyon23.net/math/ In theory Kevin's point of view should automatically lead to a theory extended all the way down to points, but it's phrased in a different language from the usual extended field theory language.

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This is a topic that people often say they're working on, but never seems to see the light of day. So, I wouldn't give much weight to off-hand statements that it's "known" --- it should be known, but talk is cheap!

There would be lots of exciting things to do with a well-presented extended Turaev-Viro model, so even if you end up duplicating other work it wouldn't matter so much, the fun would be just beginning :).

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