nLab
direct sum of vector bundles

Idea

For $E_1,E_2\to X$ two vector bundles, their direct sum over $X$, also called their Whitney sum, is the vector bundle $E_1\oplus E_2\to X$ whose fiber over any $x\in X$ is the direct sum of vector spaces of the fibers of $E_1$ and $E_2$.

Related concepts

• Stiefel-Whitney class