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).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.