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Infinite number of nontrivial links with trivial Jones polynomial
by
Louis H Kauffman
University of Illinois at Chicago
We discuss examples of nontrivial links with the trivial Jones polynomial. There is an infinite number of such examples being satellites of the Hopf link. The first such an example was noticed by M.Thistlethwaite, at the end of 2000, when he analysed 15 crossing links of two components. The question of V.F.R.Jones whether there is a nontrivial knot with the trivial Jones polynomial is still open. There is however a nontrivial virtual knot with the trivial Jones polynomial.
Date received: May 7, 2001
Copyright © 2001 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 # cahj-07.