Is 3D Quantum Gravity Equivalent to a TQFT?

[atyy]

I'd always assumed it was, since LQG spin foam models are based on BF theory. And it is typically said that in 3D it is BF, and in 4D constrained BF. The 4D quantum case is not known to be gravity, but I had thought the 3D case was.

Yet in http://math.ucr.edu/home/baez/week254.html Baez commentary on Witten's http://arxiv.org/abs/0706.3359 says "Even though Witten is now claiming 3d quantum gravity can't be a TQFT ...", which means the question was not resolved as of 2007.

Apprently, even the existence of quantum pure 3D gravity wasn't known in 2009 http://arxiv.org/abs/0906.1313 (see the fourth problem).

So is quantum 3D BF is quantum 3D gravity?

What is the status of this problem now?

 

[atyy]

I just remembered, isn't it supposed to naively be the Ponzano-Regge model, and properly regularized by the Turaev-Viro model? eg. http://arxiv.org/abs/0803.3319