3 problems

A rat-group is obtained by deleting the final relator from an Artin $n$-presentation of the trivial group, so it has a deficiency-one presentation. A knot group is characterized by…

González-Acuña's conjecture. If $A$ is an Artin $n$-presentation such that $|A|=1$, then $A\sim T$. This is one of the conjectures relating Artin presentations of the trivial group…

Exotic-manifold conjecture. Closed, exotic $4$-manifolds should appear in Artin presentation theory with second Betti number three, and this should relate to the Torelli subgroup i…