Topology Atlas | Conferences

Knots in Washington XXXVII
January 19-20, 2014
George Washington University
Washington, DC, USA

Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU and UMCP), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

Conference Homepage

The Kauffman bracket ideal for genus-1 tangles
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.