1 Answers
In the mathematical field of topology, a sphere bundle is a fiber bundle in which the fibers are spheres S n {\displaystyle S^{n}} of some dimension n. Similarly, in a disk bundle, the fibers are disks D n {\displaystyle D^{n}}. From a topological perspective, there is no difference between sphere bundles and disk bundles: this is a consequence of the Alexander trick, which implies BTop ≃ BTop . {\displaystyle \operatorname {BTop} \simeq \operatorname {BTop}.}
An example of a sphere bundle is the torus, which is orientable and has S 1 {\displaystyle S^{1}} fibers over an S 1 {\displaystyle S^{1}} base space. The non-orientable Klein bottle also has S 1 {\displaystyle S^{1}} fibers over an S 1 {\displaystyle S^{1}} base space, but has a twist that produces a reversal of orientation as one follows the loop around the base space.
A circle bundle is a special case of a sphere bundle.