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Mostrando ítems 1-10 de 32
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
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
Twisted conjugacy in braid groups
(Springer, 2014)
In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids u, v ∈ Bn and an automorphism ϕ ∈ Aut(Bn), decides whether v = (ϕ(x))−1ux for some x ∈ Bn. As a ...
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] ...
Tesis Doctoral
Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique.
(2018-09-03)
En la primera parte de esta tesis estudiamos la conjetura de genericidad: En el grafo de Cayley del mapping class group de una superficie cerrada, consideramos una bola de radio suficientemente grande centrada en el elemento ...
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.