Abstract
In this paper, we give a necessary condition for detecting (possibly punctured) closed incompressible meridionally incompressible surfaces in knot or link complements. This condition provides us a method to determine whether an arbitrary link is split or non-split based on the link diagram. We also prove that, up to isotopy, there only exist finitely many such surfaces in non-split prime almost alternating link complements. Finally, we demonstrate an application of the necessary condition by showing elementary by-hand proofs that some certain knots are small knots.
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 callDisclaimer: 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.
