differentiable vector bundle

(see also *Chern-Weil theory*, parameterized homotopy theory)

**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**

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.

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

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