A Geometric Approach to a Class of Equilibrium Existence Theorems*

In this paper we propose a general mathematical approach to existence problems in economics based on the geometry of vector bundles and the methods of intersection theory. The existence problem is formulated as: Does an approximate vector bundle admit a non-zero continuous section? The motivation and major application comes from incomplete market theory, where the appropriate vector bundle has, as one of the components of its base space, a Grassmanian manifold. Several general existence results are offered. One infinite dimensional generalization is included.