5 problems

Knot-biquandle completeness conjecture. The knot biquandle is a complete invariant of virtual link type: if two knotlike biquandle presentations are related by Tietze moves, then t…

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…

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

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