Inverse bundle

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

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

$E\oplus E^{\prime }\cong M\times {ℝ}^n.$

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

References

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