About Goto's method showing surjectivity of word maps Abdelrhman ElkasapyAndreas Thom 22Eword mapsLie groups Let $\mathbf{F}$ be the free group on two letters. For $\omega\in\mathbf{F}$, we study the associated word map $\omega\colon\SU(n)\times\SU(n)\to\SU(n)$. Extending a method of Got\^o, we show that, for $\omega$ not in the second derived subgroup $\mathbf{F}^{(2)}$ of $\mathbf{F}$, there are infinitely many $n\in\mathbb{N}$ such that the associated word map $\omega:\SU(n)\times\SU(n)\to\SU(n)$ is surjective. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5391 10.1512/iumj.2014.63.5391 en Indiana Univ. Math. J. 63 (2014) 1553 - 1565 state-of-the-art mathematics http://iumj.org/access/