Inverse bundle

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

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


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

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