Browsing by Author "González-Meneses López, Juan"
Now showing items 1-20 of 37
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Article
A geometric characterization of the upper bound for the span of the Jones polynomial
(World Scientific, 2011-07)Let D be a link diagram with n crossings, sA and sB its extreme states and |sAD| (resp. |sBD|) the number of simple closed ...
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Article
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 ...
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Article
Basic results on braid groups
(Université Blaise Pascal, 2011)These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) ...
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Article
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.
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Final Degree Project
Clasificación de grupos cristalográficos planos
(2022-06-15)Crystallographic groups are groups whose elements are isometries of a metric space. These groups are 17 in the Euclidean ...
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Article
Closures of positive braids and the Morton-Franks-Williams inequality
(Elsevier, 2014-09-01)We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). ...
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Article
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. ...
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Article
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 ...
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Article
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 ...
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Article
Conjugacy in Garside Groups III: Periodic braids
(Elsevier, 2007-10-15)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 ...
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Article
Conjugacy problem for braid groups and Garside groups
(Elsevier, 2003-08-01)We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented ...
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Article
Generating random braids
(Elsevier, 2013-01)We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. ...
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Article
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 ...
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Article
Geometric embeddings of braid groups do not merge conjugacy classes
(Sociedad Matemática Mexicana, 2014-10)An embedding of the m-times punctured disc into the n-times punctured disc, for n > m, yields an embedding of the braid ...
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Final Degree Project
Homología de Khovanov
(2018-09)Knot theory is quite younger compare to other theories in mathematics. Even so, it is an important mathematic theory in ...
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Article
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 ...
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Article
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.
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Article
On reduction curves and Garside properties of braids
(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 ...
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PhD Thesis
On some families of links and new approaches to link homologies
(2016-03-01)Esta tesis se enmarca dentro de la Teoría de Nudos. En los Capítulos 1 y 2 se usan herramientas clásicas para estudiar las ...
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Article
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 ...