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Reference.org
Splitting principle
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the splitting principle is a technique used to reduce questions about <a href="/facts/Vector_bundle/cXACAa1I">vector bundles</a> to the case of <a href="/facts/Line_bundle/CupAl1ft">line bundles</a>. In the theory of vector bundles, one often wishes to simplify computations, for example of <a href="/facts/Chern_classes/Tw2WD5hM">Chern classes</a>. Often computations are well understood for line bundles and for direct sums of line bundles. Then the splitting principle can be quite useful. </p>