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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Knot invariants from categorical quandles and Alexander modules
by
Masahico Saito
University of South Florida
Coauthors: J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi

A categorical quandle, called a strict 2-quandle, is a category and also is a quandle satisfying certain conditions. Definitions, constructions of examples, and the fundamental strict 2-quandle are reviewed. Colorings of knot diagrams by strict 2-quandles are defined, and a virtual knot invariant is defined in a manner similar to Alexander modules. Applications and variations of the invariant are given for virtual knots and spatial graphs.

Date received: November 28, 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-22.