The pure virtual braid group is quadratic

Derivative Varieties and the Pure Braid Group

Geometric Presentations for the Pure Braid Group

We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged “convexly”, which is why we describe them as geometric presentations. Motivated by a presentation for the full braid group that we call the “rotation presentation”, we introduce...

un 2 00 9 ON THE PURE VIRTUAL BRAID GROUP PV

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 w...

Pure Virtual Braids Homotopic to the Identity Braid

Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing changes. We recall the pure virtual braid group. We then describe the set of pure virtual braids that are homotopic to the identity braid.

The Chen Groups of the Pure Braid Group

A b st r ac t . The Chen groups of a group are the lower central series quotients of its maximal metabelian quotient. We show that the Chen groups of the pure braid group Pn are free abelian, and we compute their ranks. The computation of these Chen groups reduces to the computation of the Hilbert series of a certain graded module over a polynomial ring, and the latter is carried out by means o...