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math.GT2003
Braids in trivial braid diagrams
Patrick Dehornoy
We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every A…
math.GR2003
The group of fractions of a torsion free lcm monoid is torsion free
Patrick Dehornoy
We improve and shorten the argument given in(Journal of Algebra, vol.~210 (1998) pp~291--297). Inparticular, the fact that Artin braid groups are torsion free now follows from Gars…