Inverse bundle

Short description: Topology in mathematics

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

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

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

References

• Hatcher, Allen (2003), Vector Bundles & K-Theory (2.0 ed.), http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html