Let $F$ be a free group on 2 generators and $G = \operatorname{SL}(d,\mathbb{C})$. A word $w \in F$ induces the word map $\mathrm{ev}_w: G \times G \to G$.

Can we find some (generic) conditions on $A,B \in G$ such that, for all $w \in F$, the differential of $\mathrm{ev}_w$ is surjective at $(A,B)$ ?

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