PlanetMath: subbundle

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (230)
Orphanage
Unclass'd
Unproven (519)
Corrections (16)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

subbundle

(Definition)

Given a vector bundle $\pi \!:\! \mathcal E \rightarrow M$ , a subbundle $\mathcal E^\prime$ is a subset of the total space, $\mathcal E^\prime \subset \mathcal E$ , so that

$\displaystyle \pi\vert_{\mathcal E^\prime}\!:\! \mathcal E^\prime \rightarrow M$

is a vector bundle, and for each point $p\in M$ , the fibre at

$\displaystyle {\pi\vert_{\mathcal E^{\prime}}}^{-1}(p) = \mathcal E^\prime_p$

is a vector subspace of $\mathcal E_p = \pi^{-1}(p)$

"subbundle" is owned by guffin.

(view preamble)

Other names:

sub-bundle, vector sub-bundle, vector subbundle, sub-vector bundle, sub vector bundle

Also defines:

subbundle

Keywords:

subbundle, vector bundle, sub-bundle, sub-vector bundle

Log in to rate this entry.
(view current ratings)

Cross-references: vector subspace, fibre, point, subset, vector bundle
There are 7 references to this entry.

This is version 1 of subbundle, born on 2007-03-18.
Object id is 9094, canonical name is Subbundle.
Accessed 1701 times total.

Classification:

AMS MSC:	14F05 (Algebraic geometry :: homology theory :: Vector bundles, sheaves, related constructions)
	55R25 (Algebraic topology :: Fiber spaces and bundles :: Sphere bundles and vector bundles)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact