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Artículo
New presentations of surface braid groups
(World Scientific Publishing, 2001)
In this paper we give new presentations of the braid groups and the pure braid groups of a closed surface. We also give an algorithm to solve the word problem in these groups, using the given presentations.
Artículo
Vassiliev invariants for braids on surfaces
(American Mathematical Society, 2004)
We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of ...
Artículo
On the structure of the centralizer of a braid
(Elsevier, 2004)
The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and ...
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 ...