Topology Atlas | Conferences

Knots in Washington XLI
December 4-6, 2015
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

Conference Homepage


The Kauffman Polynomial of Periodic Links
by
Kyle Istvan
Louisiana State University
Coauthors: Khaled Qazaqzeh, Ayman Aboufattoum

A periodic link has a diagram that is invariant under a finite-order rotation in the plane. I will define a necessary condition for a link to be p-periodic, for odd prime p. It takes the form of a congruence between a specialization of the 2-variable Kauffman polynomial of a link and that of the link's mirror image. The result is derived using a state sum formula for the 2-variable polynomial, and can be used to verify (for example) Traczyk's result that the knot 10101 is not 7-periodic.

Date received: October 29, 2015

Copyright © 2015 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 # cblw-21.