Extended TQFT's and Quantum Gravity

Understand

This paper gives a definition of an extended topological quantum field theory (TQFT) as a weak 2-functor Z: nCob_2 -> 2Vect, by analogy with the description of a TQFT as a functor Z: nCob -> Vect.

• We also show how to obtain such a theory from any finite group G.
• This theory is related to a topological gauge theory, the Dijkgraaf-Witten model.
• To give this definition rigorously, we first define a bicategory of cobordisms between cobordisms.