4 problems

Let $\bfF$ denote the category of finitely generated free groups. Consider the functor … that assigns to each bottom tangle $T:m\to n$ the homomorphism $(i_T)_*:F_n\to F_m$. The fu…

Milnor-invariant conjecture. One should have

Set $v=\exp\frac{h}{2}$ and $q=v^2$, and let $J_T$ denote the universal $sl_2$ invariant of a bottom tangle. Let $(\bar U_q^{ev})\;\hat {}^{\;\hat \otimes n}$ be the subalgebra int…

Set $v=\exp\frac{h}{2}$ and $q=v^2$, and let $J_T$ denote the universal $sl_2$ invariant of a bottom tangle. For an $n$-component bottom tangle, let…