Cotangent bundle

This article defines a basic construct that makes sense on any differential manifold
View a complete list of basic constructs on differential manifolds

Definition

The cotangent bundle of a differential manifold is the dual bundle to its tangent bundle. In other words, it is a bundle whose fiber at every point is the dual vector space to the tangent bundle.

Facts

Sections

A section of this bundle is termed a: differential 1-form
The sheaf of sections is termed the: sheaf of differential 1-forms

Dual bundle

The dual bundle to this vector bundle is termed the: tangent bundle