Abstract
In this paper we obtain a basis-free method for determining the general form of quadratic maps over R between spheres. We show that all quadratic maps (over certain R-lattices) between spheres are Hopf maps, and that the classical Hopf fibrations, S 2 m−1 → S m , for m=2, 4, 8, are the unique nontrivial maps over Z, up to action by the orthogonal group.
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