10 problems

Giroux-torsion vanishing conjecture. If

Let $\phi$ be the flow under consideration, let $G_+$ be its associated graph, and let $SFC(\phi,\mathcal{C})$ and $CA(\phi)$ be the chain complexes described above, where…

Let $Y$ be a 3-manifold. A left-orderable fundamental group is a fundamental group $\pi_1(Y)$ admitting a strict total order invariant under left multiplication. An L-space is a 3-…

Positive-half TQFT conjecture. The TQFT assigning $(\operatorname{Rep}(H),\otimes)$ to a point recovers both aspects of the $\mathfrak{psl}(1|1)$ Chern–Simons TQFT and aspects of d…

Let $F_{g,p}$ be the surface of genus $g$ with $p\geq 1$ boundary components, viewed with all boundary components as punctures labeled by $V(0,0)_{\overline{0}}$. Let…

Let $M$ be a knot manifold. Write $\mathcal{S}(M)$ for the set of slopes on $\partial M$, $\mathcal{D}_{ord}^{wk}(M)$ for the set of weakly order-detected slopes, and $LO(M)$ for t…

Concordance conjecture for sums of torus knots. If a connected sum of possibly several torus knots is concordant to an $L$-space knot, then it is concordant to a positive torus kno…

NLS–LO–CTF equivalence conjecture. The conditions NLS, LO, and CTF are equivalent.

Let $G$ be a grid diagram, and let a formal complex structure on $G$ be a combinatorial count of domains on the grid satisfying the constraints imposed by positivity of intersectio…

Let $K$ be a knot in $S^{3}$. A knot is $\rho$-degenerate when its reduced spectral sequence converges at $\underline{E}_{1}$ and the induced filtration $\underline{\rho}$ is const…