Crystallographic groups are groups whose elements are isometries of a metric space. These groups are 17 in the Euclidean ...

En este trabajo repasaremos algunas definiciones y resultados básicos de la Teoría de Grupos y trataremos de utilizarlos ...

We show that, generically, finding the k-th root of a braid is very fast. More precisely, we provide an algorithm which, ...

We study the centralizer of a braid from the point of view of Garside theory, showing that generically a minimal set of ...

En la primera parte de esta tesis estudiamos la conjetura de genericidad: En el grafo de Cayley del mapping class group ...

Knot theory is quite younger compare to other theories in mathematics. Even so, it is an important mathematic theory in ...

The word problem, the conjugacy problem and the isomorphism problem were three fundamental problems of group theory proposed ...

We prove that the hypothetical extreme Khovanov cohomology of a link is the cohomology of the independence simplicial ...

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.

Esta tesis se enmarca dentro de la Teoría de Nudos. En los Capítulos 1 y 2 se usan herramientas clásicas para estudiar las ...

These are Lecture Notes of a course given by the author at the School Winter Braids, held at the Université de Pau et des ...

An embedding of the m-times punctured disc into the n-times punctured disc, for n > m, yields an embedding of the braid ...

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). ...

In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids ...

We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. ...

Let D be a link diagram with n crossings, sA and sB its extreme states and |sAD| (resp. |sBD|) the number of simple closed ...

These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) ...

We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy ...

In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones ...

We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is ...

We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to ...

The cycling operation is a special kind of conjugation that can be applied to elements in Artin’s braid groups, in order ...

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.

This paper is the second in a series in which the authors study the conjugacy decision problem (CDP) and the conjugacy ...

An element in Artin’s braid group Bn is said to be periodic if some power of it lies in the center of Bn. In this paper ...

In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields ...

There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We ...

In this paper we show that the singular braid monoid of an orientable surface can be embedded in a group. The proof is purely topological, making no use of the monoid presentation.

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev ...

The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base ...

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 of braids.

We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented ...

We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. ...

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 bi-orderable.

We give presentations, in terms of generators and relations, for the monoids SBn(M) of singular braids on closed surfaces. ...

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.

En este trabajo se estudian las trenzas en superficies cerradas. En primer lugar, se dan nuevas presentaciones de los ...