6 problems

Projective-plane braid stopping conjecture. The lower central series of ${\mathbf B}_{1,m}({\mathbb P}^2)$ stops at

A link $L\subset\mathbb{S}^3$ has a generalized axis $\gamma$ with fiber surface $F$ when the complement of $\gamma$ fibers over $\mathbb{S}^1$ with fiber $F$. A $1$-extended…

Nonexistence conjecture. There is no surjective homomorphism

Let $S=S_{g,p}$ be a surface with $p\ge 0$ and $g>1$. For positive integers $m$ and $n$ with $m\neq n$, consider homomorphisms between the braid groups $B_n(S)$ and $B_m(S)$. Nonex…

Let $S$ be a compact orientable surface, let $F_n(S)$ be its $n$-th configuration space, and let … be the inclusion. Write $P_n(S)=\pi_1(F_n(S))$, let $P_n$ be the Artin pure braid…

Let $S$ be a surface, possibly with boundary, and let $F_n(S)$ be its $n$-th configuration space. The inclusion … induces a homomorphism … Let $P_n$ denote the Artin pure braid gro…