8 problems

A 2-tangle is a tangle with four boundary endpoints, and 3-move equivalence is generated by 3-moves, inverse moves, and Reidemeister moves. The four basic 2-tangles are the tangles…

Separator conjecture. The object $0$ is a separator of $\mathsf{XC}$.

Classification conjecture for prime algebraic tangles. Two prime algebraic tangles are isotopic if and only if they are related by a finite sequence of twist, flype, ring, and elem…

Let $M$ be a compact smooth $k$-manifold and let … be a smooth embedding. A tame $k$-tangle is the relevant tame embedded object in $lR^n$. Smooth embedded manifolds are genericall…

Let $M$ and $M'$ be smooth manifolds with smooth embeddings … Assume that these embeddings correspond to the same normalized tangle truss in $lR^n$. Framed stratified homeomorphism…

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.…

Let $M$ be a multigraph, and let $\mathbf{TCircD}_M$ be the free braided strict monoidal category on $M$ in which each object of $M$ is equipped with a symmetric Frobenius algebra…

Let $M$ be a multigraph, and let $\mathbf{TCircD}_M$ be the free braided strict monoidal category on $M$ in which each object of $M$ is equipped with a symmetric Frobenius algebra…