Virtual braids from a topological viewpoint

Abstract : Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual braids are in a bijective correspondence with abstract braids. Finally we demonstrate that for any abstract braid, its representative of minimal genus is unique up to compatibility and Reidemeister moves. The genus of such a representative is thus an invariant for virtual braids. We also give a complete proof of the fact that there is a bijective correspondence between virtually equivalent virtual braid diagrams and braid-Gauss diagrams.
Type de document :
Pré-publication, Document de travail
2013
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https://hal.archives-ouvertes.fr/hal-00940106
Contributeur : Bruno Aaron Cisneros de La Cruz <>
Soumis le : jeudi 18 juin 2015 - 17:58:21
Dernière modification le : mardi 12 janvier 2016 - 12:58:02

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  • HAL Id : hal-00940106, version 2
  • ARXIV : 1402.0300

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Bruno Aaron Cisneros de La Cruz. Virtual braids from a topological viewpoint. 2013. <hal-00940106v2>

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