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Browsing by Author "GonzálezMeneses López, Juan"
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On the singular braid monoid of an orientable surface [Article]
Díaz Cantos, Jerónimo; GonzálezMeneses López, Juan; Tornero Sánchez, José María (American Mathematical Society, 2004)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.

On the structure of the centralizer of a braid [Article]
GonzálezMeneses López, Juan (Elsevier, 2004)The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and ...

Ordering pure braid groups on compact, connected surfaces [Article]
GonzálezMeneses López, Juan (University of California, 200204)We prove that the pure braid groups on compact, connected, orientable surfaces are biorderable, and that the pure braid groups on compact, connected nonorientable surfaces have generalized torsion, thus they are not ...

Polynomial braid combing [Article]
Flores Díaz, Ramón Jesús; GonzálezMeneses López, Juan (Oxford University Press, 2018)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.

Presentations for the monoids of singular braids on closed surfaces [Article]
GonzálezMeneses López, Juan (Taylor & Francis, 2002)We give presentations, in terms of generators and relations, for the monoids SBn(M) of singular braids on closed surfaces. The proof of the validity of these presentations can also be applied to verify, in a new way, the ...

El problema de la palabra en los grupos de trenzas [Final Degree Work]
Aguilar Martín, Javier (20180618)The word problem, the conjugacy problem and the isomorphism problem were three fundamental problems of group theory proposed by Max Dehn. We will deal with the first one. This problem consists of: given a group G with a ...

Reducible braids and Garside theory [Article]
GonzálezMeneses López, Juan; Wiest, Bert (Geometry & Topology Publications, 2011)We show that reducible braids which are, in a Garsidetheoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a ...

Solving the conjugacy problem in Garside groups by cyclic sliding [Article]
Gebhardt, Volker; GonzálezMeneses López, Juan (Elsevier, 201006)We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well ...

Sousgroupes paraboliques et généricité dans les groupes d'ArtinTits de type sphérique. [Doctoral Thesis]
Cumplido Cabello, María (20180903)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 ...

The cyclic sliding operation in Garside groups [Article]
Gebhardt, Volker; GonzálezMeneses López, Juan (Springer, 201005)We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural ...

The nth root of a braid is unique up to conjugacy [Article]
GonzálezMeneses López, Juan (Mathematical Sciences Publishers, 20031101)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 NielsenThurston classification ...

Trenzas en superficies cerradas [Doctoral Thesis]
GonzálezMeneses López, Juan (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 ...

Twisted conjugacy in braid groups [Article]
GonzálezMeneses López, Juan; Ventura Capell, Enric (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 ...

Vassiliev invariants for braids on surfaces [Article]
GonzálezMeneses López, Juan; Paris, Luis (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 ...