Abstract
We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration. We use elementary differential geometry, and no surgery or K-theory, to carry out the construction-indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives. This result is new only for 5 dimensional spheres, but our new method of proof is elementary.
| Original language | English |
|---|---|
| Pages (from-to) | 1155-1191 |
| Number of pages | 37 |
| Journal | American Journal of Mathematics |
| Volume | 126 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Oct 2004 |
| Externally published | Yes |