Orientable vector bundle: Difference between revisions
(New page: {{vector bundle property}} ==Definition== A vector bundle over a topological space is termed '''orientable''' if it satisfies the following equivalent conditions: * The associat...) |
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* The associated [[orientation sheaf]] is trivial | * The associated [[orientation sheaf]] is trivial | ||
* For every fiber, we can choose an orientation, in such a manner that in any open neighbourhood on which the bundle is trivial, the choice of orientation is continuous (equivalently, smooth) | * For every fiber, we can choose an orientation, in such a manner that in any open neighbourhood on which the bundle is trivial, the choice of orientation is continuous (equivalently, smooth) | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Trivial vector bundle]] | |||
* [[Stably trivial vector bundle]] | |||
Revision as of 01:55, 28 February 2008
Template:Vector bundle property
Definition
A vector bundle over a topological space is termed orientable if it satisfies the following equivalent conditions:
- The associated orientation sheaf is trivial
- For every fiber, we can choose an orientation, in such a manner that in any open neighbourhood on which the bundle is trivial, the choice of orientation is continuous (equivalently, smooth)