TOPOLOGICAL QUANTUM FIELD THEORIES ASSOCIATED TO FINITE GROUPS AND CROSSED G-SETS
Using methods suggested by the work of Turaev and Viro [11, 12], we provide a detailed construction of topological quantum field theories associated to finite crossed G-sets. Our construction of theories associated to finite groups fills in some details implicit in Dijkgraaf and Witten's [3] discussion of topological gauge theories with finite gauge group, while the theories associated to finite crossed G-sets simultaneously extend Dijkgraaf and Witten's [3] results to 3-manifolds equipped with links and Freyd and Yetter's [5] construction of link invariants from crossed G-sets from links in the 3-sphere to links in arbitrary 3-manifolds. Topological interpretations of the manifold and link invariants associated to these TQFT's are provided. We conclude discussion of our results as a toy model for QFT and of their relation to quantum groups.