Abstract

For a smooth map between spheres, we are concerned with the relation between its homotopy class (topological complexity) and its dilatation (geometrical complexity). This paper (1) generalizes the results of Olivier and Roitberg on the dilatation of Hopf fibrations and the elements of the stable homotopy groups of spheres. (2) Disproves two conjectures of Olivier and Roitberg by showing that δ(2,4) < 3 and δ(3,4) = 2.

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