Hopf Fibration - Generalizations

Generalizations

The Hopf construction, viewed as a fiber bundle p: S3 → CP1, admits several generalizations, which are also often known as Hopf fibrations. First, one can replace the projective line by an n-dimensional projective space. Second, one can replace the complex numbers by any (real) division algebra, including (for n = 1) the octonions.