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An Extended Bracket Polynomial for Virtual Knots
by
Louis H. Kauffman
University of Illinois at Chicago
This talk will discuss an extension of the bracket polynomial for oriented virtual knots and links that takes values in the module generated by isotopy classes of virtual 4-regular graphs over the ring of Laurent polynomials Q[A, A-1] where Q denotes the integers. This invariant is constructed by using an oriented state expansion and keeping as much combinatorial structure in the state sum as one can. Applications of the invariant and open problems will be discussed. A special case of this invariant is the arrow polynomial of the author and Heather Dye, a variant of the Miyazawa polynomial. We will discuss applications that involve the use of both the extended bracket and the arrow polynomial.
Paper reference: arXiv:0712.2546, arXiv:0810.3858
Date received: February 14, 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 # cayk-06.