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.
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@incollection {bolton, MRKEY = {1185722},
AUTHOR = {Bolton, J. and Woodward, L. M.},
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PAGES = {143--151},
PUBLISHER = {World Sci. Publ., River Edge, NJ},
YEAR = {1992},
MRCLASS = {58E20 (58D27)},
MRNUMBER = {1185722},
MRREVIEWER = {Martin A. Guest},
ZBLNUMBER = {0838.58005},
} -
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author={Bolton, J. and Woodward, L. M.},
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author={Verdier, J.-L.},
TITLE={Two dimensional $\sigma$-models and harmonic maps from ${S}^2$ to ${S}^{2n}$},
BOOKTITLE={Group Theoretical Methods in Physics},
EDITOR={Serdaro{\u g}lu, M and {Í}n{ö}n{ü},
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@incollection {Wood:76, MRKEY = {0649784},
AUTHOR = {Wood, J. C.},
TITLE = {Harmonic maps and complex analysis},
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}
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