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Pré-Publication, Document De Travail Année : 2013

Virtual braids from a topological viewpoint

Résumé

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.
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Dates et versions

hal-00940106 , version 1 (31-01-2014)
hal-00940106 , version 2 (18-06-2015)

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