Search results for "Virtual knots"

Topological characterization of virtual braids

2015

The purpose of this thesis is to give a topological characterization of virtual braids. Virtual braids are equivalence classes of planar braid-like diagrams identified up to isotopy, Reidemeister and virtual Reidemeister moves. The set of virtual braids admits a group structure and is called the virtual braid group. In Chapter 1 we present a general introduction to the theory of virtual knots, and we discuss some properties of virtual braids and their relations with classical braids. In Chapter 2 we introduce braid-Gauss dia- grams, and we prove that they are a good combinatorial reinterpretation of virtual braids. In particular this generalizes some results known in virtual knot theory. As…