TITLE: Turaev-Viro extended TQFT
QUESTION [12 upvotes]: 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

REPLY [6 votes]: 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.