Nondegeneracy of half-harmonic maps from $\mathbb{R}$ into ${\mathbb{S}}^1$

Y. Sire, J. Wei, Y. Zheng

We prove that the standard half-harmonic map $U:\mathbb{R}\to {\mathbb{S}}^1$ defined by \begin{equation*} x\to \begin{pmatrix} \frac{x^2-1}{x^2+1} \frac{-2x}{x^2+1} \end{pmatrix} \en…