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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The framed braid group and $ 3$-manifolds


Authors: Ki Hyoung Ko and Lawrence Smolinsky
Journal: Proc. Amer. Math. Soc. 115 (1992), 541-551
MSC: Primary 57N10; Secondary 20F36, 57M07
MathSciNet review: 1126197
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1126197-1
PII: S 0002-9939(1992)1126197-1
Keywords: $ 3$-manifolds, Braid group
Article copyright: © Copyright 1992 American Mathematical Society