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Dissertation/Thesis Abstract

A Diagrammatic Multivariate Alexander Invariant of Tangles
by Kennedy, Kathleen Grace, Ph.D., University of California, Santa Barbara, 2013, 90; 3596170
Abstract (Summary)

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.

Indexing (document details)
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
Subjects: Mathematics
Keywords: Alexander, Invariant, Knot theory, Multivariable, Planar algebra, Tangle
Publication Number: 3596170
ISBN: 978-1-303-42597-4
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