4 problems

Przytycki's 4-move conjecture. Any knot is 4-equivalent to the unknot.

The unknot has trivial homology, so its Hodge Laplacian has a two-dimensional ground-state kernel. Efficient cooling conjecture. It may be possible to efficiently cool the Hodge La…

Let $K$ be a smoothly embedded $2$-sphere in $S^4$. Write $u_{\textup{st}}(K)$ for its stable unknotting number, $u_{\textup{cw}}(K)$ for its Casson–Whitney unknotting number, and…

Let $F$ be an orientable surface, let $\widetilde F$ be its universal cover, and let $c:[0,1]\to F$ be a closed smooth curve whose lift to $\widetilde F$ is injective. Call $c$ pre…