15 problems

Ohtsuki's factorial integrality conjecture. For every $n\geq 1$ and every integral homology 3-sphere $M$,

Let $\delta_n(M)\in V_n$ be the framing correction for the invariant $I_n(M)$ of a homology $3$-sphere $M$ decorated with a framing or bundled bordism. Vanishing conjecture for the…

Let $M$ be an integer homology $3$-sphere, let $\widetilde{I}_n(M)$ be the decoration-independent unframed invariant obtained by subtracting the framing correction from $I_n(M)$, a…

The p-modular TQFT structure conjecture.

Let ${\cal V}^{DF}$ be Donaldson's TQFT associated with moduli spaces of connections on a non-trivial $SO(3)$ bundle. For $x_1,x_2,\ldots$, define … Let ${\cal V}^{(D)}$ be the pol…

Let a plumbed 3-manifold be represented by an arbitrary, possibly non-reduced, plumbing, and let the associated $(q,t)$-series be specialized by taking $t\rightarrow 1$ to obtain a…

Let $M$ be a bordered 3-manifold with $n$ toroidal boundary components, equipped with a system of arcs $\mathscr{A}\subseteq M$. Let $\mathcal{X}(M,\mathscr{A})^{\mathcal{L}}$ deno…

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…

Knot-decorated decomposition conjecture. The WRT invariant satisfies

Index-factorization conjecture. The index satisfies

Categorification conjecture. There are series $\widehat Z_b(q)$, convergent for $|q|<1$, such that

Let $M$ be a homology $3$-sphere and let $\widehat{Z}_{2k,3k}(M)$ be the invariant defined from the higher-order configuration-space construction. The configuration-space integral…

Let $M$ be a homology $3$-sphere and, for each $k\geq 1$, let $\widehat{Z}_{2k,3k}(M)$ denote the invariant constructed from the higher-order configuration-space integral. Nontrivi…

Let $\mathcal{U}_\varpi=U_\varpi(\mathfrak{g})$ be a quantized universal enveloping algebra at an odd root of unity, and let $\mathcal{B}^{\pm}_\varpi$ be its Borel Hopf subalgebra…