9 problems

Let $M$ be a simply connected $3$-manifold, possibly with holes, and let $S_{2,\infty}(M)$ denote its Kauffman bracket skein module at parameter $2$ and infinity. Traczyk's conject…

Crossingless tangle basis conjecture. Crossingless tangles with $2n$ endpoints form a basis for

Let $M$ be the quaternionic manifold, obtained as the quotient of $S^3$ by the action of the quaternionic group $Q_8$, and let $S(M;\mathbb{Z}[A^{\pm1}],A)$ denote its Kauffman bra…

Let $M$ be an oriented atoroidal $3$-manifold, and let $\mathcal{S}_{2,\infty}(M)$ denote its Kauffman bracket skein module. Finite-rank conjecture. The Kauffman bracket skein modu…

Let $M$ be a compact oriented $3$-manifold. Write $\mathcal{S}_{2,\infty}(M)$ for its Kauffman bracket skein module. An incompressible surface is understood in the usual sense, and…

Let $M$ be an oriented atoroidal $3$-manifold, meaning that every incompressible torus in $M$ is parallel to the boundary. Let the Kauffman bracket skein module of $M$ be denoted b…

Let $T=(a_1^{\varepsilon_1},\dots,a_n^{\varepsilon_n})$ be a virtual rational tangle, where the $a_i$ are the tangle parameters and each $\varepsilon_i$ records the corresponding v…

Let $T$ be a virtual rational tangle, and let $C(T)$ denote its conductance. Two virtual rational tangles are $F$-equivalent when they are related by the equivalence generated by t…

Let $T$ be a rational $n$-tangle, and let $v_T$ be the vector-valued invariant with Laurent polynomial entries obtained from the Kauffman bracket. Kwon's classification conjecture.…