vector bundle, 2-vector bundle, (∞,1)-vector bundle real, complex/holomorphic, quaternionic A sphere fiber bundle is a fiber bundle whose fibers are spheres of some dimension . 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. The following appears in FSS 20, Sec. 3 (somewhat implicit in v1, explicitly in v2):