3 problems

Quotient structure conjecture. The structure of $L\!H_n/\chi^{(j+1)}$ is given by the $j\times j$ truncation of ${\mathcal M}^p_n$.

Let $\rho$ be an irreducible $d$-dimensional matrix representation of the braid group $\mathcal B_3$, with $\rho(\sigma_1)=A$ and $\rho(\sigma_2)=B$. The matrices are in ordered tr…

Let $\Vloop=\Thomp{\mathit{LB}_*}$ and $\Floop=\Thomp{\mathit{PLB}_*}$ be the generalized Thompson groups containing the loop braid groups and pure loop braid groups, respectively.…