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Recently, Bigelow defined a diagrammatic method for calculating the Alexander polynomial of a knot or link by resolving crossings in a planar algebra. In this dissertation, I will present my multivariate version of Bigelow's algorithm for the Alexander polynomial. The advantage to my algorithm is that it generalizes easily to a multivariate tangle invariant. I will also present preliminary results on the connection to Jana Archibald's tangle invariant and conclude with ideas for future research.
| Advisor: | Bigelow, Stephen J. |
| Commitee: | McCammond, Jon P., Millett, Kenneth C. |
| School: | University of California, Santa Barbara |
| Department: | Mathematics |
| School Location: | United States -- California |
| Source: | DAI-B 75/01(E), Dissertation Abstracts International |
| Source Type: | DISSERTATION |
| Subjects: | Mathematics |
| Keywords: | Alexander, Invariant, Knot theory, Multivariable, Planar algebra, Tangle |
| Publication Number: | 3596170 |
| ISBN: | 978-1-303-42597-4 |
