10 problems

A virtual link is a link represented in the virtual-link setting, and a twisted Khovanov complex is a version of the Khovanov complex adapted to twisted virtual links. Khovanov–Ras…

FKM conjecture. If two classical crossings are equivalent by such a chain, then the corresponding links are isotopic in the usual sense.

Minimality conjecture. For reduced alternating diagrams of virtual links, $n$ is the minimal number of crossings, and $h$ is the minimal genus among diagrams of the same virtual li…

Let $V_1$ and $V_2$ be non-classical, weakly prime virtual links. A connected sum is formed by joining diagrams of two links along chosen arcs; for virtual links this operation can…

A checkerboard framing is an extension of a checkerboard coloring for a virtual link diagram; consider any two checkerboard framings of the same diagram. Dye's conjecture. Any two…

Non-surjectivity conjecture. Not every welded $m$-link is isotopic to the image under $T_{mn}$ of some virtual $m$-link.

Minimal genus conjecture for virtual links. Given a virtual link $L$, any minimal crossing diagram for it has minimal genus.

Minimal-volume chain-link conjecture. For $3\leq n\leq 10$, the minimally twisted $n$-chain link yields the minimal volume of a non-classical virtual link of $n-2$ components.

Monotonicity conjecture. The function $V_{min}(g)$ is monotone increasing for $g\geq 0$.

Minimal volume conjecture. The minimal volume non-classical virtual link is the virtual trefoil, with a volume of approximately $5.33349$.