THE FRAMED BRAID GROUP AND 3-MANIFOLDS

Abstract

The framed braid group on n strands is defined to be a semidirect product of the braid group B(n) and Z(n) . Framed braids represent 3-manifolds in a manner analogous to the representation of links by braids. Consider two framed braids equivalent if they represent homeomorphic 3-manifolds. The main result of this paper is a Markov type theorem giving moves that generate this equivalence relation.