7 problems

Let $D_{n,m}^i$ and $E_{n,m}^i$ be the diagrams defined in the paper, and consider the saddle cobordism … at the crossing corresponding to the last letter $\sigma_i$. Surjectivity…

Equality conjecture. If each component of $F$ intersects $M_1$, then, as $\mathbb{Z}$-graded bimodules over $(A_{EF}(M_2),A_{EF}(M_1))$,

Let $K\subset S^3$ be a knot, let $S^3_{-n}(K)$ be obtained by $(-n)$-surgery, and let $W$ be the natural cobordism from $S^3$ to $S^3_{-n}(K)$. Let $t_i:H_2(W_{-n})\to\mathbb{Z}$…

Let $K$ be a knot in $S^3$. A concordance is a cobordism of minimal intrinsic complexity, and it has minimal extrinsic complexity when it has no index $2$ Morse critical points. Sl…

Let $(M,\gamma)$ be a balanced sutured manifold, and let $\mathcal{W}=(W=M\times[0,1],Z=\partial M\times[0,1],[\xi])$ be the trace sutured cobordism from…

Let $M$ be a hyperbolic $4$-cobordism with boundary components $N_0$ and $N_1$. Suppose that $N_0$ and $N_1$ are highly symmetric to each other, both topologically and geometricall…

Grid-cobordism functoriality conjecture. Grid diagram maps induce maps on $\operatorname{HFK}^-$ that are invariant with respect to marked smooth isotopy classes of surfaces.