9 problems

Let $L$ be a link, let $\mathsf{H}_q(L)$ be its HOMFLYPT difference module, let $[L]$ be its distinguished link class, and let $\mathsf{ev}\colon \mathsf{H}(L)\to \mathcal{F}_r$ be…

Let $T$ be a framed oriented $r$-component tangle in ${\mathbb{R}}^3_{x\geq 0}$, let $N(\varLambda_T)$ be its specified neighborhood, and let $H$ denote the reference subspace used…

Let $K$ be a knot in $bS^3$, let $bbSigmad_2K$ be its 2-fold branched covering, and let $X(bbSigmad_2K)$ be the $bSL_2(bC)$ character variety of $bpi_1(bbSigmad_2K)$. Write…

Let $\Phi$ be the chain map from the degree-zero knot contact-homology complex at $Q=1$ to the cord algebra of a knot. Cord-algebra isomorphism conjecture. The map $\Phi$ induces a…

Let $K\subset\mathbb{R}^3$ be a knot, let $HC_*(K)$ be its contact homology algebra, and let … Let $\overline{V_K}$ denote the closure of $V_K$. Polynomial-component conjecture. Th…

Let $K$ be a knot in $S^3$, and let $f(U)$ be the polynomial determined by the branch of the zero locus of $\operatorname{Aug}_K$ near $(\lambda,\mu,U)=(0,U,U)$ through … Here…

Let $K\subset S^3$ be a knot, and let $\mathbf{A}_K(e^x,e^p,Q)$ denote the three-variable $Q$-deformed $A$-polynomial associated with the mirror construction for the resolved conif…

Let $K$ be a knot, and let $\operatorname{Aug}_K(\lambda,\mu,U)$ be its three-variable augmentation polynomial. When the $U=1$ slice of the augmentation variety has a maximal-dimen…

Let $K$ be a knot. The augmentation variety $V_K$ is the set of augmentation values in $(\mathbb{C}^*)^3$, and the augmentation polynomial is defined when the maximal-dimensional p…