9 problems

Free abelian link-group conjecture. Then $L$ is welded equivalent to the unlink.

The degree-zero/degree-one conjecture.

Injectivity conjecture. If two classical spatial graphs are virtually equivalent, then they are classically equivalent.

A classical spatial graph is a spatial graph represented by a classical graph diagram, and two such graphs are virtually equivalent or classically equivalent according to the virtu…

Free welded non-triviality conjecture. The knot $S$ shown in Figure $19$ is non-trivial in free welded theory.

An even, degree-one Vassiliev invariant is a function $V$ on virtual knots such that $V(K_+)-V(K_-)=0$ for even crossings and $V(K+)-V(K-) e 0$ for odd crossings. Nonexistence conj…

Let $T=(a_1^{\varepsilon_1},\dots,a_n^{\varepsilon_n})$ be a virtual rational tangle, where the $a_i$ are the tangle parameters and each $\varepsilon_i$ records the corresponding v…

Let $T$ be a virtual rational tangle, and let $C(T)$ denote its conductance. Two virtual rational tangles are $F$-equivalent when they are related by the equivalence generated by t…

Virtualization produces virtual knots with unit Jones polynomial, and the examples under consideration are non-trivial. Non-classicality conjecture. All non-trivial examples produc…