4 problems

Let $\Sigma_g$ be a genus-$g$ Heegaard surface in $S^3$, with $g\geq 4$, and let $\mathcal{R}(\Sigma_g)$ denote its reducing sphere complex. Its vertices are isotopy classes of red…

Goeritz-conjugacy conjecture. Any eyeglass twist on $T_g$ is Goeritz conjugate to a Powell move.

Eyeglass-twist conjecture. Any eyeglass twist on $T_g$ is a Powell move.

Disk-pair association conjecture. There is a topological method associating to every such vertex $(a,b)$ a Powell equivalence class of homeomorphisms…