Invariantes esfericos de 2-categorias e invariantes de 4-variedades

We introduce the notion of a spherical 2-category, which is a monoidal 2-category with some extra structure, and study some fundamental properties of these 2-categories. Then we show how to use spherical 2-categories for the construction of state-sum invariants of compact oriented piece-wise linear four-dimensional manifolds without boundary (4-manifolds for short). In order to define such a state-sum for a given 4-manifold we choose a triangulation. Our construction is such that the value of the state-sum does not depend on this choice, so it yields and invariant of the 4-manifold. The results obtained in this dissertation indicate that our construction generalizes all other known constructions of state-sum invariants of 4-manifolds. Finally we give a large class of examples of spherical 2-categories and work out the related state-sums in detail. Assuming a certain technical result, still to be proved, about the equivalence of two definitions of monoidal 2-categories, we find that the 2-categories in our example are algebraic models for homotopy 3-typesAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1249-074 Lisboa, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga