1998/06/05 by J. Scott Carter, Louis H. Kauffman, Carter, J. Scott +3
Mathematics · #18D05 #57Q15 #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #math.CT #math.GT #msc:18D05 #msc:57Q15
paper · pdf · doi:10.48550/arxiv.math/9806023
80 pages, 57 figures
arxiv created 1998/06/05 · arxiv updated 2009/11/30
Crane and Frenkel proposed a state sum invariant for triangulated 4-manifolds.They defined and used new algebraic structures called Hopf categories for their construction. Crane and Yetter studied Hopf categories and gave some examples using group cocycles that are associated to the Drinfeld double of a finite group. In this paper we define a state sum invariant of triangulated 4-manifolds using Crane-Yetter cocycles as Boltzmann weights. Our invariant generalizes the 3-dimensional invariants defined by Dijkgraaf and Witten and the invariants that are defined via Hopf algebras. We present diagrammatic methods for the study of such invariants that illustrate connections between Hopf categories and moves to triangulations.