Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

5-2018

Committee Chair or Co-Chairs

Frederick Norwood

Committee Members

Frederick Norwood, Robert Gardner, Rodney Keaton

Abstract

The Jones polynomial is a special topological invariant in the field of Knot Theory. Created by Vaughn Jones, in the year 1984, it is used to study when links in space are topologically different and when they are topologically equivalent. This thesis discusses the Jones polynomial in depth as well as determines a general form for the closure of any braid in the braid group B2 where the closure is a knot. This derivation is facilitated by the help of the Temperley-Lieb algebra as well as with tools from the field of Abstract Algebra. In general, the Artin braid group Bn is the set of braids on n strands along with the binary operation of concatenation. This thesis also shows results of the relationship between the closure of a product of braids in B2 and the connected sum of the closure of braids in B2. Results on the topological invariant of tricolorability of closed braids in B2 and (2,n) torus links along with their obverses are presented as well.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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