un 2 00 9 ON THE PURE VIRTUAL BRAID GROUP PV
نویسنده
چکیده
In this article, we investigate various properties of the pure virtual braid group PV3. From its canonical presentation, we obtain a free product decomposition of PV3. As a consequence, we show that PV3 is residually torsion free nilpotent, which implies that the set of finite type invariants in the sense of GoussarovPolyak-Viro is complete for virtual pure braids with three strands. Moreover we prove that the presentation of PV3 is aspherical. Finally we determine the cohomology ring and the associated graded Lie algebra of PV3.
منابع مشابه
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Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [17]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...
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