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Some new developments in quandle cohomology theory - computations, applications and quandles in tensor categories
by
Masahico Saito
University of South Florida
Coauthors: Too Many To List
Continuing Scott Carter's talk, more recent developments in the theory of quandle cohomology and its applications will be discussed. In particular, an overview will be given on computations of quandle cocycle invariants with polynomial cocycles, and their data base presented in our web site. An application in tangle embeddings is presented as a demonstration on how the data base can be used for applications of quandle cocycle invariants to topological properties of knots. Then structures similar to quandles in coalgebras and Hopf algebras will be discussed. For these structures, coboundary operators are constructed in low dimensions, towards their cohomology theories. This is an analogue of the Hochschild double complex for bialgebras. Deformation theoretical aspects and diagrammatics for cocycles will be discussed for both Hochschild cohomology and these quandle coboundary operators.
Date received: April 25, 2006
Copyright © 2006 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 # casv-09.