Clutching construction

In topology, a branch of mathematics, the clutching construction is a way of constructing fiber bundles, particularly vector bundles on spheres.

Consider the sphere ${\displaystyle S^{n}}$ as the union of the upper and lower hemispheres ${\displaystyle D_{+}^{n}}$ and ${\displaystyle D_{-}^{n}}$ along their intersection, the equator, an ${\displaystyle S^{n-1}}$.

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