4 problems

A knot is given as the closure of a braid on four strands, and the unknot recognition problem asks whether the resulting knot is isotopic to the unknot. Braid-index four polynomial…

For a fixed dimension, algorithmic recognizability asks whether there is an algorithm deciding whether a triangulated ball is a ball. Algorithmic unrecognizability conjecture for 4…

Let $B$ be a branched surface in a compact triangulated atoroidal irreducible $3$-manifold $N$. A branched surface is quasi-hyperbolic if it does not carry any sphere or torus but…

Three-fragment generic-move conjecture. Generic moves on $3$ fragments enable one to decide the isotopy of knots in general.