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Artículo
The cyclic sliding operation in Garside groups
(Springer, 2010-05)
We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural ...
Artículo
Solving the conjugacy problem in Garside groups by cyclic sliding
(Elsevier, 2010-06)
We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well ...
Artículo
The nth root of a braid is unique up to conjugacy
(Mathematical Sciences Publishers, 2003-11-01)
We prove a conjecture due to Makanin: if α and β are elements of the Artin braid group Bn such that α k = β k for some nonzero integer k, then α and β are conjugate. The proof involves the Nielsen-Thurston classification ...