Inverse bundle
From HandWiki
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 [math]\displaystyle{ E \rightarrow M }[/math] be a fibre bundle. A bundle [math]\displaystyle{ E' \rightarrow M }[/math] is called the inverse bundle of [math]\displaystyle{ E }[/math] if their Whitney sum is a trivial bundle, namely if
- [math]\displaystyle{ E \oplus E' \cong M \times \mathbb{R}^n. \, }[/math]
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
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