3 problems

Pure twin group conjecture. The group $PT_n$ is a right-angled Artin group for each $n\geq 3$.

Let $T_n$ be the twin group generated by involutions $s_1,\dots,s_{n-1}$ with $s_i s_j=s_j s_i$ whenever $|i-j|\geq 2$, and let $PT_n$ be the kernel of the natural homomorphism…

Let $PT_n$ denote the pure twin group on $n$ strands. In particular, the preceding results identify $PT_4$ as a free group, and the rank formula gives rank 31 for…