The study of knot invariants is a large and active area of research in the field of knot theory. In the early 1990s, Russian mathematican Victor Vassiliev developed a series of numerical knot invariants, now known as Vassiliev invariants. These invariants have sparked a great deal of interest in the mathematical community, and it is conjectured that, together, they formulate a complete knot invariant. The computation of these invariants is largely algebraic, and unfortunately the values do not appear to describe any intrinsic properties of the knot. In this thesis, a geometric interpretation of the second Vassiliev invariant is provided by examining occurrances of five distinct points on the knot that lie on a common circle in the ambient space. This process is then extended to include an analysis of six-point cocircularities of knots as well. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/3405 |
| Date | 15 July 2011 |
| Creators | Flowers, Garret |
| Contributors | Budney, Ryan David |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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