# Cotangent bundle

From Diffgeom

This article defines a basic construct that makes sense on any differential manifold

View a complete list of basic constructs on differential manifolds

## Contents

## 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-formThe 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