A crystallographic quotient of the framed braid group and associated flat manifolds

Ênio Leite, Oscar Ocampo, Paulo Cesar Cerqueira dos Santos Júnior +1

We study the quotient of the framed braid group $F{B}_n$ by the commutator subgroup of the framed pure braid group $F{P}_n$. We prove that $$ \frac{FB_n}{[FP_n,FP_n]}\cong\mathbb Z^n\r…