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Mostrando ítems 1-10 de 16
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
Ordering pure braid groups on compact, connected surfaces
(University of California, 2002-04)
We prove that the pure braid groups on compact, connected, orientable surfaces are bi-orderable, and that the pure braid groups on compact, connected non-orientable surfaces have generalized torsion, thus they are not ...
Artículo
Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups
(American Mathematical Society, 2005)
There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We improve an algorithm, due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by applying a ...
Artículo
Computation of centralizers in braid groups and Garside groups
(Consejo Superior de Investigaciones Científicas, 2003)
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9] ...
Artículo
Conjugacy in Garside groups II: Structure of the ultra summit set
(European Mathematical Society, 2008)
This paper is the second in a series in which the authors study the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in Garside groups. The ultra summit set USS(X) of an element X in a Garside group ...
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.
Tesis Doctoral
Trenzas en superficies cerradas
(2000)
En este trabajo se estudian las trenzas en superficies cerradas. En primer lugar, se dan nuevas presentaciones de los grupos de trenzas en superficies cerradas, que son mucho más simples que las ya conocidas, y que tienen ...
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
Conjugacy in Garside groups I: Cyclings, powers, and rigidity
(European Mathematical Society, 2007)
In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where ‘rigid’ means that ...
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.