The dimension and structure of the space of harmonic 2-spheres in the $m$-sphere

Abstract

We prove the conjecture, posed in 1993 by Bolton and Woodward, that the dimension of the space of harmonic maps from the 2-sphere to the $2n$-sphere is $2d+n^2$. We also give an explicit algebraic method to construct all harmonic maps from the 2-sphere to the $m$-sphere.