nLab differentiable vector bundle

Idea

A differentiable vector bundle is a vector bundle in the context of differential geometry: a differentiably varying collection of vector space over a given differentiable manifold.

All this for some specified degree of differentiability. If one demands arbitrary differentiabiliy then one speaks of smooth vector bundles over smooth manifolds.

Examples

For $X$ a differentiable manifold, then its tangent bundle $T X \to X$ is a differentiable vector bundle, see this lemma.

Related concepts

• topological vector bundle

• differentiable vector bundle