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Organizers |
Theory of Quandles
by
J. Scott Carter
University of South Alabama
Coauthors: Masahico Saito
I will give the definition of a G-family of quandles that was introduced by Ishii, Iwakiri, Jang, and Oshiro. Given such a family for a fixed group, G, there is a quandle structure on the set X ×G where X is the underlying set of the G-family. There are natural ways of coloring knotted trivalent oriented spacial graphs and embedded foams in 4-space by G-families of quandles.
The relations induced by moves to these objects suggests a cohomology theory that incorporates classical group cohomology and quandle homology. The singularities that represent the graph and foam moves are dual to prismatic sets. Consequently, it is very easy to see that the boundary maps square to zero. I will sketch the definition of cocycle invariants associated to foams and to spacial graphs.
Date received: April 22, 2011
Copyright © 2011 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 # cbcc-19.