IUMJ

Title: About Goto's method showing surjectivity of word maps

Authors: Andreas Thom and Abdelrhman Elkasapy

Issue: Volume 63 (2014), Issue 5, 1553-1565

Abstract:

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.