nLab differentiable vector bundle

Contents

Context

Bundles

bundles

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

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 XX a differentiable manifold, then its tangent bundle TXXT X \to X is a differentiable vector bundle, see this lemma.

Last revised on August 1, 2018 at 12:07:14. See the history of this page for a list of all contributions to it.