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      N-tangle Kanenobu knots with the same Jones polynomials

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      Author
      Kutluay, Deniz
      Advisor
      Degtyarev, Alexander
      Date
      2010
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      It is still an open question if there exists a non-trivial knot whose Jones polynomial is trivial. One way of attacking this problem is to develop a mutation on knots which keeps the Jones polynomial unchanged yet alters the knot itself. Using such a mutation; Eliahou, Kauffmann and Thistlethwaite answered, affirmatively, the analogous question for links with two or more components. In a paper of Kanenobu, two types of families of knots are presented: a 2- parameter family and an n-parameter family for n ≥ 3. Watson introduced braid actions for a generalized mutation and used it on the (general) 2-tangle version of the former family. We will use it on the n-tangle version of the latter. This will give rise to a new method of generating pairs of prime knots which share the same Jones polynomial but are distinguishable by their HOMFLY polynomials.
      Keywords
      Braid action
      Jones polynomial
      Kanenobu knot
      Mutation
      Tangle
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      http://hdl.handle.net/11693/15071
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      • Dept. of Mathematics - Master's degree 124
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