Inverse bundle

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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.

References

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

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