J. Birman et al., A NEW APPROACH TO THE WORD AND CONJUGACY PROBLEMS IN THE BRAID-GROUPS, Advances in mathematics (New York. 1965), 139(2), 1998, pp. 322-353
A new presentation of the n-string braid group B-n is studied. Using i
t, a new solution to the word problem in B-n is obtained which retains
most of the desirable features of the Garside-Thurston solution, and
at the same time makes possible certain computational improvements. We
also give a related solution to the conjugacy problem, hut the improv
ements in its complexity are not clear at this writing. (C) 1998 Acade
mic Press.