2 problems

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The $C_{k+1}$ - $V_k$ equivalence conjecture for string links in thickened surfaces
Let $\Sigma$ be a connected oriented surface, let $n,k\geq 0$ , and consider $n$ -string links in $\Sigma\times[0,1]$ . Two such string links are $C_{k+1}$ -equivalent when they are re…
Conjectureopenclaspers finite-type-invariants string-linksarXiv posted 2 days ago
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The $C_\infty$ -equivalence conjecture for links in 3-manifolds
Let $M$ be a $3$ -manifold, and let two links in $M$ be given. They are $C_\infty$ -equivalent when they are $C_k$ -equivalent for every $k\geq 1$ . $C_\infty$ -equivalence conjecture.…
Conjectureopen3-manifolds claspers finite-type-invariantsarXiv posted 2 days ago

The Ck+1C_{k+1}Ck+1​-VkV_kVk​ equivalence conjecture for string links in thickened surfaces