The framed braid group and 3-manifolds

Ko, Ki Hyoung; Smolinsky, Lawrence

doi:10.1090/S0002-9939-1992-1126197-1

The framed braid group and $3$-manifolds
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by Ki Hyoung Ko and Lawrence Smolinsky PDF

Proc. Amer. Math. Soc. 115 (1992), 541-551 Request permission

Abstract:

The framed braid group on $n$ strands is defined to be a semidirect product of the braid group ${B_n}$ and ${{\mathbf {Z}}^n}$. 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.

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