| Autor: |
de La Cruz, Bruno Aaron Cisneros |
| Rok vydání: |
2014 |
| Předmět: |
|
| 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: |
|
