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KNOTS IN WASHINGTON XXI: Skein modules, Khovanov homology and Hochschild homology
December 9-11, 2005
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU)

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Knots with the same Jones polynomial
by
Kerry Luse
GWU
Coauthors: Yongwu Rong

This talk is motivated by the open question of whether or not the Jones polynomial can detect knottedness. We show that given a knot of the form K = K̅m# Km, one can construct K¢ such that K and K¢ are distinct, but indistinguishable by the Jones polynomial. This example is motivated by the work of Eliahou, Kauffman, and Thistlethwaite [2001], Kanenobu [1986], and Watson [2005].

Date received: December 8, 2005

Copyright © 2005 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 # carw-23.