Splitting principle

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 — Let be a vector bundle of rank over a paracompact space . There exists a space , called the flag bundle associated to , and a map such that

Splitting principle

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 — Let be a vector bundle of rank over a paracompact space . There exists a space , called the flag bundle associated to , and a map such that