Topological Higher Gauge Theory - from BF to BFCG theory

Understand

We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory.

• First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter.
• Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians.
• We then explain that two of these models are already familiar from the literature: the SigmaPhiEA-model of 3-dimensional gravity coupled to topological matter, and also a 4-dimensional model of BF-theory coupled to topological matter.