6 problems

Let ${\mathsf H}_r$ be the freely generated ribbon Hopf algebra in the symmetric monoidal category $\langle {\mathsf H}_r\rangle$, and for $n\geq 0$ let … be the universal invarian…

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. (i) If all Milnor …

Habiro's conjecture. The universal $sl_2$ invariant $J_T$ belongs to

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…