Computational search for nontrivial knots with unit Jones polynomial
Tuzun, Robert Erol
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This thesis details a strategy for a computational search for a non-trivial knot with trivial Jones polynomial, based in large part on the recent strategy of Yamada. New methods or improvements to existing methods have been found for enumerating trivializable algebraic tangles, for enumerating Conway polyhedra and for eliminating some from consideration, for computing individual Kauffman brackets, and for computing all possible Kauffman brackets given a set of tangles. Many miscellaneous strategies have been found for eliminating certain sets of knots from requiring calculation or for speeding up the calculations.