5 problems

Let defining graphs encode Coxeter groups, and let diagram twist equivalence be the equivalence relation generated by diagram twists over the family of all defining graphs. Diagram…

Strong twist conjecture. If $U\subseteq A$ is an Artin generating set with $R_S=R_U$, then $S$ and $U$ are twist equivalent.

Weak twist conjecture. If $U\subseteq A$ is an Artin generating set with $R_S=R_U$, then $\Gamma_S$ and $\Gamma_U$ are twist equivalent.

Torus-link/circular-group isomorphism conjecture. For all $n,m\in\mathbb{N}^*$, this morphism is an isomorphism. The claim generalises the previously established coprime case; the…

Brady's isomorphism conjecture. The groups $A_{\Gamma}$ and $A_{\Gamma'}$ are isomorphic if and only if $\Gamma'$ can be obtained from $\Gamma$ by a series of diagram twists.