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Published online by Cambridge University Press: 20 November 2018
Guest–Ohnita and Crawford have shown the path-connectedness of the space of harmonic maps from ${{S}^{2}}$ to $\text{C}{{P}^{n}}$ of a fixed degree and energy. It is well known that the $\partial$ transform is defined on this space. In this paper, we will show that the space is decomposed into mutually disjoint connected subspaces on which $\partial$ is homeomorphic.