  We consider diagrams of links in $S^2$ obtained by projection from $S^3$ with
the Hopf map and the minimal crossing number for such diagrams. Knots admitting
diagrams with at most one crossing are classified. Some properties of these
knots are exhibited. In particular, we establish which of these knots are
algebraic and, for such knots, give an answer to a problem posed by Fiedler.
