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math.GT2000
Does the Jones polynomial detect the unknot?
Stephen J. Bigelow
We address the question: Does there exist a non-trivial knot with a trivial Jones polynomial? To find such a knot, it is almost certainly sufficient to find a non-trivial braid on…
math.GR2000
Braid Groups are Linear
Stephen J. Bigelow
The braid groups B_n can be defined as the mapping class group of the n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is the induced action on a certai…