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Browsing by Author "GonzálezMeneses López, Juan"
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A geometric characterization of the upper bound for the span of the Jones polynomial [Article]
GonzálezMeneses López, Juan; González Manchón, Pedro María (World Scientific, 201107)Let D be a link diagram with n crossings, sA and sB its extreme states and sAD (resp. sBD) the number of simple closed curves that appear when smoothing D according to sA (resp. sB). We give a general formula for the ...

A geometric description of the extreme Khovanov cohomology [Article]
GonzálezMeneses López, Juan; González Manchón, Pedro María; Silvero Casanova, Marithania (Cambridge University Press, 201806)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 nontrivial extreme Khovanov ...

Basic results on braid groups [Article]
GonzálezMeneses López, Juan (Université Blaise Pascal, 2011)These are Lecture Notes of a course given by the author at the FrenchSpanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be ...

Biorderings on pure braided Thompson's groups [Article]
Burillo Puig, José; GonzálezMeneses López, Juan (200803)In this paper it is proved that the pure braided Thompson’s group BF admits a biorder, analog to the biorder of the pure braid groups.

Closures of positive braids and the MortonFranksWilliams inequality [Article]
GonzálezMeneses López, Juan; González Manchón, Pedro María (Elsevier, 20140901)We study the MortonFranksWilliams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is a orthonormal basis for the ...

Computation of centralizers in braid groups and Garside groups [Article]
Gonçalves Soares Franco, Nuno María; GonzálezMeneses López, Juan (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] ...

Conjugacy in Garside groups I: Cyclings, powers, and rigidity [Article]
Birman, Joan S.; Gebhardt, Volker; GonzálezMeneses López, Juan (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 ...

Conjugacy in Garside groups II: Structure of the ultra summit set [Article]
Birman, Joan S.; Gebhardt, Volker; GonzálezMeneses López, Juan (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 ...

Conjugacy in Garside Groups III: Periodic braids [Article]
Birman, Joan S.; Gebhardt, Volker; GonzálezMeneses López, Juan (Elsevier, 20071015)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 we prove that all previously known algorithms for solving the conjugacy search problem in Bn are ...

Conjugacy problem for braid groups and Garside groups [Article]
Gonçalves Soares Franco, Nuno María; GonzálezMeneses López, Juan (Elsevier, 20030801)We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside ...

Generating random braids [Article]
Gebhardt, Volker; GonzálezMeneses López, Juan (Elsevier, 201301)We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. The complexity of this algorithm is polynomial in the number of strands and in the length of ...

Geometric approaches to braid groups and mapping class groups [Article]
GonzálezMeneses López, Juan (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 ...

Geometric embeddings of braid groups do not merge conjugacy classes [Article]
GonzálezMeneses López, Juan (Sociedad Matemática Mexicana, 201410)An embedding of the mtimes punctured disc into the ntimes punctured disc, for n > m, yields an embedding of the braid group on m strands Bm into the braid group on n strands Bn, called a geometric embedding. The main ...

Homología de Khovanov [Final Degree Work]
Rivera Bustos, Ana Alicia (201809)Knot theory is quite younger compare to other theories in mathematics. Even so, it is an important mathematic theory in the topology field. Besides, it seems to have relation with other fields of knowledge like biology or ...

Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups [Article]
GonzálezMeneses López, Juan (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 ...

New presentations of surface braid groups [Article]
GonzálezMeneses López, Juan (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.

On reduction curves and Garside properties of braids [Article]
GonzálezMeneses López, Juan (American Mathematical Society, 2011)In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. ...

On some families of links and new approaches to link homologies [PhD Thesis]
Silvero Casanova, Marithania (20160301)Esta tesis se enmarca dentro de la Teoría de Nudos. En los Capítulos 1 y 2 se usan herramientas clásicas para estudiar las propiedades de ciertas familias de enlaces y las relaciones de inclusión entre ellas. En los Capítulos ...

On the centralizer of generic braids [Article]
GonzálezMeneses López, Juan; Valladares García, Dolores (De Gruyter, 201811)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 ...

On the cycling operation in braid groups [Article]
GonzálezMeneses López, Juan; Gebhardt, Volker (Elsevier, 20080906)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 ...