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The Kauffman bracket ideal for genus-1 tangles
by
Susan M. Abernathy
Louisiana State University
A genus-1 tangle is a 1-manifold with two boundary components properly embedded in the solid torus. A genus-1 tangle G embeds in a link L if we can complete G to L via a 1-manifold in the complement of the solid torus containing G. A natural question to ask is: given a tangle G and a link L, how can we tell if G embeds in L? We define the Kauffman bracket ideal, which gives an obstruction to tangle embedding, and outline a method for computing a finite list of generators for this ideal. We also give an example of a genus-1 tangle with non-trivial Kauffman bracket ideal and discuss how the concept of partial closures relates to this ideal.
Date received: November 30, 2013
Copyright © 2013 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 # cbid-09.