On recognition of virtual braids
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 267-286

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The virtual braid group $VB_n$ containing the Artin braid group $B_n$ as a subgroup is studied. A complete invariant constructed earlier on $B_n$ is extended to $VB_n$. It is conjectered that this invariant is also complete.
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     author = {V. O. Manturov},
     title = {On recognition of virtual braids},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a17/}
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V. O. Manturov. On recognition of virtual braids. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 267-286. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a17/