Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories

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dc.creatorCarter, J. Scott
dc.creatorKauffman, Louis H.
dc.creatorSaito, Masahico
dc.date1998-06-05
dc.date.accessioned2026-07-07T05:24:56Z
dc.date.available2026-07-07T05:24:56Z
dc.descriptionCrane 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.
dc.description80 pages, 57 figures
dc.identifierhttps://arxiv.org/abs/math/9806023
dc.identifierhttp://arxiv.org/abs/math/9806023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77001
dc.subjectGeometric Topology
dc.subjectCategory Theory
dc.subject57Q15, 18D05
dc.titleStructures and Diagrammatics of Four Dimensional Topological Lattice Field Theories
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