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|
|School Location:||United States -- California|
|Source:||DAI-B 75/01(E), Dissertation Abstracts International|
|Keywords:||Alexander, Invariant, Knot theory, Multivariable, Planar algebra, Tangle|
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