Abstract
It is shown that every knot or link is the set of complex tangents of a 3 3 -sphere smoothly embedded in the 3 3 -dimensional complex space. We show in fact that a 1 1 -dimensional submanifold of a closed orientable 3 3 -manifold can be realised as the set of complex tangents of a smooth embedding of the 3 3 -manifold into the 3 3 -dimensional complex space if and only if it represents the trivial integral homology class in the 3 3 -manifold. The proof involves a new application of singularity theory of differentiable maps.
Sign-in/Register to access full text options 
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.
