Inverse bundle

In mathematics, the inverse bundle of a fibre bundle is its inverse with respect to the Whitney sum operation.

Let ${\displaystyle E\rightarrow M}$ be a fibre bundle. A bundle ${\displaystyle E'\rightarrow M}$ is called the inverse bundle of ${\displaystyle E}$ if their Whitney sum is a trivial bundle, namely if

${\displaystyle E\oplus E'\cong M\times \mathbb {R} ^{n}.\,}$

Any vector bundle over a compact Hausdorff base has an inverse bundle.

• Hatcher, Allen (2003), Vector Bundles & K-Theory (2.0 ed.)