7 problems

Partial-conjugation relation conjecture. For each $1\leq i\leq n$,

Let $L(m)$ denote the string links on $m$ strands. For $n\geq 1$, let $V_n$-equivalence be the equivalence relation induced by the Vassiliev filtration, and let $C_n$-equivalence b…

The $w_k$-equivalence conjecture. Two welded string links are $w_k$-equivalent if and only if they cannot be distinguished by finite type invariants of degree $<k$.

Fix $m\geq 2$, $k\geq 1$, and $n\geq 3$. Let … be the graphing map. Graphing injectivity conjecture. The induced maps on rational homotopy and rational homology are injective: … ar…

Consider the sum of the trees depicted in Figure 8 of the source, associated to 2-component string links, with coefficients in $\mathbb Z/2\mathbb Z$. Framed Arf finite-type conjec…

Let $\mathrm{pStr}(n)$ be the monoid of pure string links. The Kirk–Livingston–Wang representation is … and let $p\mathcal W_{n,1/0}$ denote the corresponding quotient of the two-v…

Let string links be proper tangles without closed components, and let two string links have the same number of components. They are Goussarov–Habiro conjecture. Two string links of…