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.

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