A cellular topological field theory

2017, January 20
A. S. Cattaneo, P. Mnev and N. Reshetikhin
arXiv Preprint
We present a construction of cellular BF theory (in both abelian and non-abelian 
variants) on cobordisms equipped with cellular decompositions. Partition functions
of this theory are invariant under subdivisions, satisfy a version of the quantum 
master equation, and satisfy Atiyah-Segal-type gluing formula with respect to 
composition of cobordisms.