6 problems

Let $m$ be an integer and let $\hat{\mathcal{D}}$ be the $0$-crossing diagram of the unknot. A diagram of the unknot $\mathcal{D}$ has $n$ crossings if…

Let the Freedman–He–Wang unknot be the unknot diagram discussed in the cited source, and let an unknotting sequence be a sequence of Reidemeister moves connecting it to a round dia…

Define the extended Reidemeister moves to be the standard Reidemeister move set together with a fourth move, in which $A$ is a compact set whose interior remains fixed relative to…

A knot projection is the image of a generic immersion of a circle into the $2$-sphere, and deformations of types $1$, $2$, and $3$ are the local replacements analogous to Reidemeis…

Let $K$ be a virtual knot, and let $D$ and $D'$ be diagrams of $K$. The generalized Reidemeister-move conjecture. There exist two diagrams $D$ and $D'$ such that every sequence of…

Let a generic immersion be a map $S^{1}\rightarrow\mathbb{R}^{2}$ with only generic singularities, and let Reidemeister moves 1, 2, and 3 be the usual planar moves on immersed curv…