If we construct a rank vector bundle formula_35 which is a finite whitney sum of vector bundles we can construct a sphere bundle formula_36 whose fibers are the spheres formula_37. Then, we can use the Serre spectral sequence along with the Euler class to compute the integral cohomology of . The formula_3-page is given by formula_39. We see that the only non-trivial differentials are given on the formula_40-page and are defined by cupping with the Euler class formula_41. In this case it is given by the top chern class of formula_35. For example, consider the vector bundle formula_43 for a K3 surface. Then, the spectral sequence reads as