Section of a vector bundle

Summary

A section of a vector bundle chooses one vector in the fiber over each point of the base. The choice varies smoothly with the point. Vector fields are sections of the tangent bundle, and differential forms are sections of bundles of alternating forms. The sections of a vector bundle form a vector space, and in fact a module over the ring of smooth functions on the base. Many objects of geometry and physics, such as fields in gauge theory, are sections of suitable bundles.