## Tangent bundle |

In **tangent bundle** of a *M*. As a set, it is given by the ^{[note 1]} of the *M*. That is,

where denotes the

defined by . This projection maps each tangent space to the single point .

The tangent bundle comes equipped with a *M* is framed if and only if the tangent bundle *TM* is stably trivial, meaning that for some trivial bundle *E* the *TM* ⊕ *E* is trivial. For example, the *n*-dimensional sphere *S ^{n}* is framed for all

- role
- topology and smooth structure
- examples
- vector fields
- higher-order tangent bundles
- canonical vector field on tangent bundle
- lifts
- see also
- notes
- references
- external links

One of the main roles of the tangent bundle is to provide a domain and range for the derivative of a smooth function. Namely, if *f* : *M* → *N* is a smooth function, with *M* and *N* smooth manifolds, its *Df* : *TM* → *TN*.

Other Languages

català: Fibrat tangent

Deutsch: Tangentialbündel

español: Fibrado tangente

français: Fibré tangent

한국어: 접다발

հայերեն: Շոշափողակոյտ

italiano: Fibrato tangente

Nederlands: Raakbundel

日本語: 接束

polski: Wiązka styczna

português: Fibrado tangente

русский: Касательное расслоение

svenska: Tangentknippe

Türkçe: Tanjant demet

українська: Дотичне розшарування

中文: 切丛