Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories
Copyright policy )Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories
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.
80 pages, 57 figures
- Florida State University United States
- University of Chicago United States
- Florida Southern College United States
- University of Illinois at Chicago United States
- University of Illinois at Chicago United States
Mathematics(all), 4-manifold, Triangulating manifolds, Mathematics - Category Theory, Geometric Topology (math.GT), triangulation, Topology of the Euclidean \(4\)-space, \(4\)-manifolds, diagrammatic method, 57Q15, 18D05, Mathematics - Geometric Topology, topological lattice field theory, FOS: Mathematics, Hopf category, Category Theory (math.CT), Topological field theories in quantum mechanics, Crane-Yetter cocycle
Mathematics(all), 4-manifold, Triangulating manifolds, Mathematics - Category Theory, Geometric Topology (math.GT), triangulation, Topology of the Euclidean \(4\)-space, \(4\)-manifolds, diagrammatic method, 57Q15, 18D05, Mathematics - Geometric Topology, topological lattice field theory, FOS: Mathematics, Hopf category, Category Theory (math.CT), Topological field theories in quantum mechanics, Crane-Yetter cocycle
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