Topology Atlas | Conferences

Some Corollaries of Manturov's projection Theorem
by
Vladimir Chernov
Dartmouth College

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 an ordinary knot K the values of these invariants are less or equal than the classical canonical genus g_c(K) and the bridge number b(K) respectively. We use Manturov's projection from the category of virtual knot diagrams to the category of ordinary knot diagrams, to show that for every ordinary knot type K we have g_vc(K)=g_c(K) and vb(K)=b(K).

Date received: November 25, 2017

Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboj-15.