Orientable manifold

Thiss article defines a property that can be evaluated for a differential manifold, invariant under diffeomorphisms
View other properties of differential manifolds

Definition

A differential manifold is termed orientable if it satisfies the following equivalent condition:

• Its tangent bundle is an orientable vector bundle
• The local homology sheaf is a trivial $\mathbb {Z}$-bundle

Relation with other properties

Stronger properties

• Parallelizable manifold
• Stably parallelizable manifold
• Simply connected manifold