nLab
sphere fiber bundle

Contents

Context

Bundles

Contents

Idea

A sphere fiber bundle is a fiber bundle whose fibers are spheres S nS^n of some dimension nn.

Often, but not always, this is considered in homotopy theory or even in stable homotopy theory, hence for fibers which have the (stable) homotopy type of a sphere, in which case one speaks of spherical fibrations. See there for more.

Examples

A key example of sphere fiber bundles are the unit sphere bundles inside of real vector bundles that are equipped with orthogonal structure: the bundles whose fibers are the unit spheres in the corresponding fiber of the given real vector bundle.

These appear in the discussion of Thom spaces and hence of Thom spectra, as well as in the discussion of wave front sets.

Last revised on March 5, 2019 at 02:28:51. See the history of this page for a list of all contributions to it.