Orientable manifold: Difference between revisions
(New page: {{differential manifold property}} ==Definition== A differential manifold is termed '''orientable''' if it satisfies the following equivalent condition: * Its tangent bundle is ...) |
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* Its [[tangent bundle]] is an [[orientable vector bundle]] | * Its [[tangent bundle]] is an [[orientable vector bundle]] | ||
* The [[local homology sheaf]] is a trivial <math>\mathbb{Z}</math>-bundle | * The [[local homology sheaf]] is a trivial <math>\mathbb{Z}</math>-bundle | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Parallelizable manifold]] | |||
* [[Stably parallelizable manifold]] | |||
* [[Simply connected manifold]] | |||
Revision as of 01:52, 28 February 2008
Thiss article defines a property that can be evaluated for a differential manifold, invariant under diffeomorphisms
View other properties of differential manifolds
Definition
A differential manifold is termed orientable if it satisfies the following equivalent condition:
- Its tangent bundle is an orientable vector bundle
- The local homology sheaf is a trivial -bundle