nLab
differentiable vector bundle
Contents
Context
Bundles
bundles

covering space

retractive space

fiber bundle , fiber ∞-bundle

numerable bundle

principal bundle , principal ∞-bundle

associated bundle , associated ∞-bundle

vector bundle , 2-vector bundle , (∞,1)-vector bundle

real , complex /holomorphic , quaternionic

topological , differentiable , algebraic

with connection

bundle of spectra

natural bundle

equivariant bundle

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

Last revised on August 1, 2018 at 12:07:14.
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