Geometric representation of cohomological classes
Let C be a site, L a sheaf defined on C, elements of H^0(C,L), H^1(C,L), and H^2(C,L) classify or are geometric representations of respectively, sections, torsors, and gerbes defined on C bounded by L. This geometric objects are used in differential geometry where torsors or differential bundles, allow to study topological and differential properties of manifolds, in algebraic geometry, gerbes or stacks are fundamental objects in the study of moduli spaces. In theoretical physics the action which describe the evolution of a string is a function of the holonomy of a gerbes. Representations of higher classes are motivated by many examples as to find a geometric description of the action which describe the evolution of a brane in physics. The purpose of this talk is to describe how we can use a sequence of fibered categories to define geometric representations of cohomological classes.