2 problems

Let $n\ge 2$. Let $F_n$ be a free group with rank $n$ and $F$ be a free group. Let $g,h:F_n\to F$ be monomorphisms. Stallings equalizer conjecture. Then … This conjecture was open…

Let $n\ge 3$, let $F_n$ be a free group of rank $n$, and let $F$ be a free group. Let $g,h:F_n\to F$ be monomorphisms. Sharp equalizer rank conjecture. Then … The paper constructs…