9 problems

Let $A$= $S^1\times[0,1]$ be the annulus, let $L\subset A\times I$ be an annular link, and let $\mathrm{wrap}(L)$ be the minimal geometric intersection number between $L$ and a mer…

Let $L$ be an annular link, let $k\in\mathbb Z$ be its winding grading, and let $\mathbb F$ be a field of characteristic zero. Denote by…

Let $L$ be a $p$-periodic link for an odd prime $p$, and let $\overline{L}$ be its quotient link, treated as an annular link with the axis of symmetry as the annular axis. Write…

Let $L$ be a link, let $r\geq 2$, and let ${\mathcal X}^r_{\mathbb{A}_\mathfrak{q}}(L)$ be the $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum refining quantum annular homology…

Let $L$ be an annular link, let $Kh_{\mathbb{A}_\mathfrak{q}}(L)$ denote its quantum annular homology, and let ${\mathcal X}^r_{\mathbb{A}_\mathfrak{q}}(L)$ be the associated spect…

Let $\tilde L$ be a 2-periodic link in $S^3$ with quotient link $L$. Write $Kh$ for Khovanov homology and $AKh$ for annular Khovanov homology, both over $\mathbb{F}_2$, and let…

Let $W_k$ denote the invariants in the decomposition associated with the spectral sequence from sutured annular Khovanov homology to ordinary Khovanov homology. Collapse conjecture…

Let $\sigma_n^{\epsilon_n}\sigma_{n-1}^{\epsilon_{n-1}}\cdots\sigma_1^{\epsilon_1}$ be a stabilized unknot, where each $\epsilon_i=\pm1$, and let $W_0$ denote the corresponding inv…

Let ${\text{SKh}}$ denote sutured annular Khovanov homology, and let $U_q({\mathfrak{sl}_2})$ denote the quantum group whose categorification supplies the relevant bimodules. Hochs…