Joan S. Birman, K. H. Ko, J. S. Lee
Published 1997-12-02, updated 1998-04-07Version 2
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, but the improvements in its complexity are not clear at this writing.
Comments: This updated version of "A new approach to the word problem in the braid groups" contains a new section on the conjugacy problem. 31 pages
Journal: Advances Math.139(1998),322-353
A fast algorithm to the conjugacy problem on generic braids
On the conjugacy problem in braid groups: Garside theory and subsurfaces
Conjugacy problem for braid groups and Garside groups
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