On the two-parabolic subgroups of sl(2,c)

We consider homomorphisms $H_{t}$ from the free group $F$ of rank $2$ onto the subgroup of SL$(2,\mathbb{C})$ that is generated by two parabolic matrices. Up to conjugation, $H_{t}$ depends only on one complex parameter $t$. We study the possible relators, that is, the words $w\in F$ with $w\neq 1$...