6 problems

Let $\widehat{K}$ be a rationally null-homologous knot in $\widehat{Y}$, and let $\hat{\mu}$ and $\hat{\lambda}$ be the slope data used in the construction. Given $m\in\mathbb{Z}$…

Let $Y$ be a closed three-manifold, let $K\subset Y$ be a knot, and let $Y_n(K)$ denote the result of $n$-surgery on $K$. Let $W_n^\prime(K)$ be the cobordism defined above, and le…

Let $K$ be a knot, let $r$ be the surgery parameter, and write … Let … be the Ramanujan theta function. Regularized $+1/r$-surgery conjecture. When the $+1/r$-surgery formula of Gu…

Let $K$ be a knot and consider the $+1$-surgery formula of Gukov and Manolescu for the invariant $\hat{Z}$. Regularized $+1$-surgery conjecture. When the $+1$-surgery formula conve…

Let $K\subset S^3$ be a knot, and let $f_\rho^G(K)$ denote the coefficient indexed by the Weyl vector in the higher-rank knot series. Higher-rank 0-surgery formula. … In particular…

Let $K\subset S^3$ be a knot, let $G$ be a root system with positive roots $\Delta^+$, and let $\mathcal{L}_{p/r}^{(b)}$ denote the surgery transform appearing in the formula. High…