Complexity of relations in the braid group
Abstract
We show that for any given n, there exists a sequence of words ak in the generators sigma1, ... sigman-1 of the braid group Bn, representing the identity element of Bn, such that the number of braid relations of the form sigmai sigmai+1 sigmai = sigmai+1 sigmai sigmai+1 needed to pass from ak to the empty word is quadratic with respect to the length of ak.
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