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The planar algebra associated to an alternating link and its Jones Polynomial.
by
Stella Huerfano
University of Bogota, Columbia
The Jones polynomial of a non-split alternating link is alternating. A generalization of this result to the case of non-split alternating
tangles is presented. The Jones polynomial of tangles is valued in a certain skein module, where the alternating condition for tangles can be described.
It has been shown by Hernando Burgos (see his PhD thesis) that this
condition is "preserved" by the Jones polynomial associated to
the diagrams of the single positive and negative crossings,
and it is also preserved by appropriately chosen "alternating"
planar algebra compositions.
As a result, we demonstrate that this condition, for links, reduces to the alternation of the coefficients of the Jones polynomial.
Date received: January 12, 2009
Copyright © 2009 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 # caxq-64.