Autor: |
de La Cruz, Bruno Aaron Cisneros |
Rok vydání: |
2014 |
Předmět: |
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Zdroj: |
Journal of Knot Theory and Its RamificationsVol. 24, No. 06, 1550033 (2015) |
Druh dokumentu: |
Working Paper |
DOI: |
10.1142/S0218216515500339 |
Popis: |
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. |
Databáze: |
arXiv |
Externí odkaz: |
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