nLab
differentiable vector bundle

Context

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.

Revised on June 8, 2017 06:03:20 by Urs Schreiber (46.183.103.17)