SOME COROLLARIES OF MANTUROV'S PROJECTION THEOREM

Abstract

In our works with Stoimenow, Vdovina and with Byberi, we introduced the virtual canonical genus g vc (K) and the virtual bridge number vb (K) invariants of virtual knots. One can see from the definitions that for a classical knot K the values of these invariants are less than or equal to the classical canonical genus gc(K) and the bridge number b(K) respectively. We use Manturov's projection from the category of virtual knot diagrams to the category of classical knot diagrams, to show that for every classical knot type K we have g vc (K) = gc(K) and vb (K) = b(K).