3 problems

Trivial-kernel conjecture. The kernel of $\eta$ is trivial; equivalently, no nontrivial singular braid in $SB_n$ maps to zero in $\mathbb{C}B_n$. This conjecture asks whether the n…

Birman's desingularization-map conjecture. The map $\psi$ is an embedding. This conjecture connects singular braids with Vassiliev invariants and quantum groups; it was proved affi…

Birman's conjecture. The map $\eta$ is injective.