It has been 10 years since the author introduced groups $G_{n}^{k}$ depending on two natural numbers $n>k$ and constructed invariants of many configuration spaces valued in such groups. https://www.arxiv.org/abs/1501.05208 . The first two natural invariants dealt with braids on n strands, $n>3$, valued in $G_{n}^{3}$ and $G_{n}^{4}$. We shall discuss how to construct similar invariants for n-component links and describe various possible ways what to do with knots (single component).  The approach uses closed braids and Markov moves. Many unsolved problems will be formulated.