3 problems

Perturbation index conjecture. The topological index of $F'$ is $n+1$.

Let $S$ be a genus $n$ Heegaard surface of $S^3$, and let its topological index be the smallest integer $k$ such that $\pi_{k-1}(\mathcal{D}(S))$ is non-trivial, where…

Let $S$ be an $(n+1)$-bridge sphere for the unknot in $S^3$, and let its topological index be the smallest integer $k$ such that $\pi_{k-1}(\mathcal{D}(S))$ is non-trivial, where…