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Mostrando ítems 1-10 de 10
Artículo
On the cycling operation in braid groups
(Elsevier, 2008-09-06)
The cycling operation is a special kind of conjugation that can be applied to elements in Artin’s braid groups, in order to reduce their length. It is a key ingredient of the usual solutions to the conjugacy problem in ...
Artículo
Geometric approaches to braid groups and mapping class groups
(Cellule Mathdoc, 2015)
These are Lecture Notes of a course given by the author at the School Winter Braids, held at the Université de Pau et des Pays de L’Adour (France), on February 2015. It is explained how mapping class groups, and in particular ...
Artículo
A geometric description of the extreme Khovanov cohomology
(Cambridge University Press, 2018-06)
We prove that the hypothetical extreme Khovanov cohomology of a link is the cohomology of the independence simplicial complex of its Lando graph. We also provide a family of knots having as many non-trivial extreme Khovanov ...
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
Bi-orderings on pure braided Thompson's groups
(2008-03)
In this paper it is proved that the pure braided Thompson’s group BF admits a bi-order, analog to the bi-order of the pure braid groups.
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
On the centralizer of generic braids
(De Gruyter, 2018-11)
We study the centralizer of a braid from the point of view of Garside theory, showing that generically a minimal set of generators can be computed very efficiently, as the ultra summit set of a generic braid has a very ...
Artículo
Polynomial braid combing
(Oxford University Press, 2018)
We prove that, for n ≥ 3, the minimal dimension of a model of the classifying space of the braid group Bn, and of the pure braid group Pn, with respect to the family of virtually cyclic groups is n.
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 ...