Whitney sum formula for Chern classes
= Whitney sum formula for Chern classes
{c}
{title2=$c(E\oplus F)=c(E)c(F)$}
The <Total Chern class> of a direct sum of complex <vector bundles> is the product of their total Chern classes. In each degree, $c_k(E\oplus F)=\sum_{i+j=k}c_i(E)\smile c_j(F)$. The degree-zero class is one, classes beyond the bundle rank vanish, and a trivial bundle has total class one.