10 problems

Let $Y$ be a closed, oriented $3$-manifold and $K\subset Y$ a knot. Let $HFK'_2(Y,K;\mathbb{C})$ be the homology of the mapping-cone complex … and let $I^\sharp(Y,K;\mathbb{C})$ de…

Let $T$ be a 2-tangle, let $R_\pi(T)$ be its holonomy-perturbed traceless character variety, and let $P^*$ be the pillowcase with its singular points removed. A bounding cochain is…

Sutured instanton–Heegaard Floer equivalence conjecture. For every balanced sutured manifold $(M,\gamma)$, there is an isomorphism

Let $T$ be a pointed 2-tangle and let $P^*\cong\partial(D^3,T)$ be the pillowcase. Write $I(T)$, $I^\natural(T)$ and $I^\sharp(T)$ for the proposed instanton-theoretic immersed cur…

Let $T$ be a 2-tangle, let $R_\pi(T)\looparrowright P^*$ be its holonomy-perturbed traceless character variety, and let $b\in \mathit{CF}(R_\pi(T),R_\pi(T))$. Let…

Let $Y$ be a rational homology sphere, let $E$ be the bundle used to define the equivariant instanton complex, let $R$ be the coefficient ring, and let $\sigma$ be a choice of sign…

Let $\Sigma$ be a closed foam in $\R^{3}$, and let $S$ be its underlying closed pre-foam. Let $\Jsharp(\Sigma)$ denote the instanton-homological evaluation of $\Sigma$, and let…

Let $S$ be a closed pre-foam, namely an abstract finite $2$-dimensional cell complex with foam local structure, possibly with tetrahedral points and dots. Define $\Jflat(S)\in\F$ b…

Let $K$ be a web in $\R^{3}$, meaning an embedded trivalent graph, and let $\Jsharp(K)$ be the associated finite-dimensional vector space over the field $\F$ of two elements. A Tai…

Let $(X,K)$ be a knot in a homology $3$-sphere, and choose a $2$-tangle decomposition $(X,K)=(Y,T)\cup(D,U)$ as in the paper. Let $P$ denote the pillowcase, let $R_\pi(Y,T)$ be the…