Abstract
The purpose of these lectures is to present an introduction to some of the fundamental elements of “classical knot theory” surrounding a description of the new families of spatial invariants derived from the 1985 discovery by V.F.R. Jones, [Jon1,2]. These finite integral Laurent polynomial invariants have provided insights into classical questions of knot theory. Their subsequent generalizations have given new invariants of 3-manifolds. Taken together these ideas form the basis of a new combinatorial theory of knots and links and invariants of 3-manifolds. The topics have been selected with an eye towards potential applications in the topological theory of fluid mechanics. In particular, I believe that the construction of satellite knots or links, especially cables, might be of particular interest in the study of closed curves arising in fluid dynamics and have, therefore, made a special effort to highlight those occasions in which this construction arises.
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.
