UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Knots, tangles and braid actions Watson, Liam Thomas


Recent work of Eliahou, Kauffmann and Thistlethwaite suggests the use of braid actions to alter a link diagram without changing the Jones polynomial. This technique produces non-trivial links (of two or more components) having the same Jones polynomial as the unlink. In this paper, examples of distinct knots that can not be distinguished by the Jones polynomial are constructed by way of braid actions. Moreover, it is shown in general that pairs of knots obtained in this way are not Conway mutants, hence this technique provides new perspective on the Jones polynomial, with a view to an important (and unanswered) question: Does the Jones polynomial detect the unknot?

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.