Topology Atlas | Conferences

Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

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A Graphical Bracket Polynomial for Virtual Knots
by
Louis H. Kauffman
Univeristy of Illinois at Chicago

The invariant of virtual knots discussed in this talk is a relative of the Arrow Polynomial and Extended Bracket Polynomials discussed in arXiv:0712.2546 and arXiv:0810.3858. We analyze the oriented state expansion of the bracket polynomial and find that for knots in thickened surfaces and for virtual knots (and links) there is a stronger invariant obtained by a system of state reduction that retains much of the oriented structure. The graphical bracket G[K] takes values in virtual graphs with coefficient polynonmials, and will be used to determine the minimal genus of various examples. Progress in categorification will be discussed.

Paper reference: arXiv:0712.2546, arXiv:0810.3858

Date received: November 5, 2008

Copyright © 2008 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-13.