Topology Atlas | Conferences

Knots in Washington XXXI; Categorification, Quandles, Quantum knots and Quantum computing
December 3-5, 2010
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU, NSF), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Categorification of the Jones-Wenzl Projectors
by
Ben Cooper
University of Virginia
Coauthors: Slava Krushkal

We construct chain complexes P_n within Dror Bar-Natan's geometric category, whose graded Euler characteristic is the Jones-Wenzl projector p_n in the Temperley-Lieb algebra. These P_n are essentially unique and satisfy a graphical calculus up to homotopy. Consequences of our construction include families of knot invariants corresponding to higher representations of Uqsu(2) and a categorification of quantum spin networks.

Paper reference: arXiv:1005.5117

Date received: November 15, 2010

Copyright © 2010 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 # cbbr-13.