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Conference on Knot Theory and Its Applications to Physics and Quantum Computing; 60th birthday of Jozef H. Przytycki
January 6-9, 2015
University of Texas at Dallas
Richardson, TX, USA

Organizers
Mieczyslaw K. Dabkowski (UTD) Tobias Hagge (UTD) Valentina S. Harizanov (GWU) Viswanath Ramakrishna (UTD) Radmila Sazdanovic (NCSU) Adam S. Sikora (SUNYUB)

Conference Homepage


Reasons to love Chebyshev knots and billiard table diagrams
by
Moshe Cohen
Technion - Israel Institute of Technology

Jones and Przytycki showed that Lissajous knots are equivalent to billiard knots in a cube; however not all knots are Lissajous. Recently Koseleff and Pecker developed an analogous parametrization using Chebyshev polynomials and showed that all knots can arise in this way.

We highlight some facets of this model and use it to compute the Jones polynomials of 2- and 3-bridge knots.

Supported in part by the funding from the European Research Council under the European Union’s Seventh Framework Programme, Grant FP7-ICT-318493-STREP.

Date received: December 23, 2014

Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-70.