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Presentations of surface braid groups by graphs

Paolo Bellingeri, Vladimir Vershinin (2005)

Fundamenta Mathematicae

We extend and generalise Sergiescu's results on planar graphs and presentations for the braid group Bₙ to other topological generalisations of Bₙ.

Pure virtual braids homotopic to the identity braid

H. A. Dye (2009)

Fundamenta Mathematicae

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.

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