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math.GT2002
Obstructions to trivializing a knot
Joan S. Birman, John A. Moody
The recent proof by Bigelow and Krammer that the braid groups are linear opens the possibility of applications to the study of knots and links. It was proved by the first author an…
math.GT2002
Stabilization in the Braid Groups (with applications to transverse knots)
Joan S. Birman, William W. Menasco
Withdrawn and replaced by two related manuscripts: (1) "Stabilization in the braid groups I:MTWS", published in Geometry and Topology Volume 10 (2006), 413-540, arXiv:math.GT/03102…
math.GT2002
On Markov's Theorem
Joan S. Birman, William W. Menasco
We give a new proof of Markov's classical theorem relating any two closed braid representations of the same knot or link. The proof is based upon ideas in a forthcoming paper by th…