Eric Forgy Bicategory of Cubes
I will try to work out a bicategory (mostly as an exercise for myself) on a 3-diamond. I’ll start with a simple directed 3-cube.
The general idea is to construct a bicategory such that
- objects are finite oriented 1-dimensional cell complexes
- morphisms are finite oriented 2-dimensional cell complexes between finite oriented 1-dimensional cell complexes
- 2-morphisms are finite oriented 3-dimensional cell complexes between finite oriented 2-dimensional cell complexes.
Tim: Just a thought. Quinn used cell complexes in some notes on TQFTs
Quinn F, Lectures on Axiomatic Topological Quantum Field Theory. Geometry and Quantum Field Theory, Volume 1, IAS/Park City Mathematical Series, American Mathematical Society, 1995, p. 325-453.
They should be worth checking out if you can. I do not have my copy 'to hand'.(It is in a huge pile on the otherside of the room!) He based TQFTs on more general things than manifolds, but I do not accurately rememebr the details.
Eric: Thanks Tim! I'll look up some of Quinn's stuff, but I do not have access to a library, so getting a hold of this paper will be tricky.
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