5 problems

Let $M$ be a closed and oriented $3$-manifold. For each positive integer $k$, let $Z_k(M)\in\mathbb{C}$ denote the $\operatorname{SU}(2)$ WRT invariant for $M$ at level $k$. Let…

Let $M$ be the plumbed $3$-manifold in the preceding asymptotic expansion, let $\mathcal{S}$ be the finite set of phases appearing there, and let…

Let $M$ be a rational homology sphere. For each $\operatorname{Spin}^c$ structure $b\in\operatorname{Spin}^c(M)$, suppose there are invariants $\Delta_b\in\mathbb{Q}$,…

Let $B$ be a nonsingular plumbing matrix with $|\det B|>1$, let $q=e^{2\pi i/k}$, and let $Y$ be the associated plumbed 3-manifold. Set … where $a\in\mathbb{Z}^V/B\mathbb{Z}^V$ and…

Let $\widehat{\mathfrak{G}}^0$ be the subgroup generated by the periods and Stokes jumps obtainable from a chosen initial integral $I^{\bbalpha_0}(k)$, and let $\mathfrak{G}_S$ den…