Abstract

We define a local move on a ribbon 2-knot diagram, called an HC-move. We show that it is an unknotting operation for a ribbon 2-knot, and that the application of a single HC-move to a ribbon 2-knot changes the second derivative at t=1 of its normalized Alexander polynomial by either ±2 or 0. This result is applied to the calculation of the HC-unknotting numbers of ribbon 2-knots. We also consider a relation with a 1-handle unknotting operation.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

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.