9 problems

Nontriviality conjecture. If $K$ admits a strong inversion, then there is a strong inversion on $K$ with nontrivial real knot Floer group.

Auxiliary-data invariance conjecture. The auxiliary data $\fra$ does not affect the real knot Floer groups.

Arbitrarily wide varkappa-invariant question. Does there exist a strongly invertible L-space knot $(K,\Phi)$ such that $\varkappa(K,\Phi)$ has width at least $n$?

Watson's conjecture. $K$ is an L-space knot if and only if $[?]$ is supported in a single diagonal grading

Equality conjecture. The inequality $\overline{V}_0^{\tau}(K_n)\geq n$ is an equality.

Let $(K,h)$ be a strongly invertible knot, and let $\widetilde{\operatorname{Kh}}(T_{K,h})$ be its reduced Khovanov invariant with special components denoted by…

Let $(K,h)$ be a strong inversion, and let $\varkappa(K,h)$ be the associated vector space. Let $V_\varkappa$ denote the vector space appearing in the decomposition of the special-…

Let $K$ be a knot, and let $h_1$ and $h_2$ be strong inversions on $K$. Rank invariance conjecture. The dimensions of the associated equivariant Khovanov homology groups are equal:…

Let $(K,h)$ be a strongly invertible knot. For some $\delta\in\mathbb{Z}$, let … Here the second grading is regarded as a relative $\mathbb{Z}$-grading, and $V[m,n]$ denotes the co…