7 problems

Let $K$ and $K'$ be virtual knots, and let $\mathcal{B}(K)$ and $\mathcal{B}(K')$ denote their fundamental biquandles. Two virtual knots are identified up to orientation-reversed m…

A virtual knot has an associated fundamental biquandle, an algebraic invariant defined from a virtual-knot diagram, and two virtual knots are identified up to mirror reflection whe…

For an oriented virtual knot $K$, let $\mathcal{B}(K)$ denote its fundamental biquandle, the algebraic structure associated with $K$ that encodes its Reidemeister moves. Fundamenta…

Virtual torus-knot span conjecture. The non-zero minimum of the product

Let $K_I$ be the virtual knot diagram discovered by Kishino. The paper notes that its generalized Alexander polynomial and Alexander Biquandle are trivial, while its general Biquan…

Przytycki–Vojtěchovský conjecture.

Biquandle invariants are invariants used for virtual $1$- and $2$-links. A Fox–Milnor movie is the movie technique referenced in the paper for encoding higher-dimensional knot or l…