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- Splitting_principle abstract "In mathematics, the splitting principle is a technique used to reduce questions about vector bundles to the case of line bundles.In the theory of vector bundles, one often wishes to simplify computations, say of Chern classes. Often computations are well understood for line bundles and for direct sums of line bundles. In this case the splitting principle can be quite useful. Theorem: Splitting Principle: Let be a vector bundle of rank over a manifold . There exists a space , called the flag bundle associated to , and a map such that the induced cohomology homomorphism is injective, andthe pullback bundle breaks up as a direct sum of line bundles: The line bundles or their first characteristic class are called Chern roots.The fact that is injective means that any equation which holds in (say between various Chern classes) also holds in . The point is that these equations are easier to understand for direct sums of line bundles than for arbitrary vector bundles, so equations should be understood in and then pushed down to .".
- Splitting_principle wikiPageExternalLink VBpage.html.
- Splitting_principle wikiPageID "15958803".
- Splitting_principle wikiPageRevisionID "604228391".
- Splitting_principle hasPhotoCollection Splitting_principle.
- Splitting_principle subject Category:Characteristic_classes.
- Splitting_principle subject Category:Mathematical_principles.
- Splitting_principle subject Category:Vector_bundles.
- Splitting_principle type Abstraction100002137.
- Splitting_principle type CharacteristicClasses.
- Splitting_principle type Class107997703.
- Splitting_principle type Cognition100023271.
- Splitting_principle type Collection107951464.
- Splitting_principle type Content105809192.
- Splitting_principle type Generalization105913275.
- Splitting_principle type Group100031264.
- Splitting_principle type Idea105833840.
- Splitting_principle type MathematicalPrinciples.
- Splitting_principle type Package108008017.
- Splitting_principle type Principle105913538.
- Splitting_principle type PsychologicalFeature100023100.
- Splitting_principle type VectorBundles.
- Splitting_principle comment "In mathematics, the splitting principle is a technique used to reduce questions about vector bundles to the case of line bundles.In the theory of vector bundles, one often wishes to simplify computations, say of Chern classes. Often computations are well understood for line bundles and for direct sums of line bundles. In this case the splitting principle can be quite useful. Theorem: Splitting Principle: Let be a vector bundle of rank over a manifold .".
- Splitting_principle label "Princípio de divisão".
- Splitting_principle label "Splitting principle".
- Splitting_principle sameAs Princípio_de_divisão.
- Splitting_principle sameAs m.03qj8cb.
- Splitting_principle sameAs Q7578745.
- Splitting_principle sameAs Q7578745.
- Splitting_principle sameAs Splitting_principle.
- Splitting_principle wasDerivedFrom Splitting_principle?oldid=604228391.
- Splitting_principle isPrimaryTopicOf Splitting_principle.