Skip to main content
2 of 2
edited tags
YCor
  • 63.9k
  • 5
  • 187
  • 285

Braid group and knot group

It is well known that braid groups and knot groups share many common properties. For example, they have the same $H_1$ and they are both residually finite and (hence) Hopfian. On the other hand, we know that $B_2$ and $B_3$ are isomorphic to the knot groups of unknot and trefoil knot respectively. My question is, for any $n\geq 4$, is there a knot with knot group $B_n$?

If not, how about high dimensional knot $S^n$ in $S^{n+2}$?