Abstract

Let be a knot inside a standardly embedded solid torus V in the 3-sphere S3. In the following , for nontriviality , we assume that cannot be lie in a 3-ball in V. Knotting the solid torus V in the shape of another knot as in Figure 0.1, as the image of K, we obtain a new knot K' in S3. A knot obtained in such a manner is called a satellite knot . On the other hand, twisting the solid torus V several times, we get a new knot K in S3. The purpose in this article is to give a survey of some aspects of the study of these constructions.

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.