Abstract
Let K be a classical knot in ℝ3. We can deform the diagram of K to that of a trivial knot by changing the overcrossings and undercrossings at some double points of the diagram of K. We consider the same problem for higher dimensinal knots. Let n≥2 and π:ℝn+2=ℝn+1×ℝ→ℝn+1 denote the natural projection map. A pseudo-ribbon n-knot is an n-knot f:Sn→ℝn+2 such that the self-intersection set of π◦f:Sn→ℝn+1 consists of only double points and is homeomorphic to a disjoint union of (n-1)-spheres. We prove that for n≠3,4, the projection (π◦f)(Sn)⊂ℝn+1 of any pseudo-ribbon n-knot f is the projection of a trivial n-knot.
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.
