A new approach to the word and conjugacy problems in the braid groups

Abstract

A new presentation of the n-string braid group B-n is studied. Using it, 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 improvements in its complexity are not clear at this writing. (C) 1998 Academic Press.