Topology Atlas | Conferences

Knots in Washington XXX; Categorification, Quantum knots and Quantum computing
May 19-21, 2010
George Washington University
Washington, DC, USA

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

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

A strict 2-quandle is a category in which objects and morphisms are quandles and for which the structure maps are quandle morphisms. We define the fundamental strict 2-quandle topologically as certain homotopy classes of arcs in knot complements. Knot invariants motivated from these are defined diagrammatically, using arrows in knot diagrams. Applications are given for crossing numbers of virtual knots.

Date received: May 12, 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 # cbaf-19.