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On quandle cocycles and abelian extensions associated with group extensions

Banff International Research Station for Mathematical Innovation and Discovery

Quandle cohomology and quandle extension theory is developed by modifying group cohomology and group extensions theory. In 1999, J. S. Carter, D. Jelsovsky, S. Kamada, L. Langford and M. Saito introduced an invariant by using quandle cocycles. It is helpful to study classical knots and knotted surfaces, and still many knot theorists have been studying quandle cocycle and quandle cocycle invariant. In this talk, we survey quandle cohomology and quandle extension theory, after then we study quandle 2-cocycles in a connection with group 2-cocycles. We also observe some properties of abelian extension of a quandle which is defined by a quandle 2-cocycle. This is a joint work with Y. Bae and J. S. Carter.

Mathematics; Manifolds And Cell Complexes

video/mp4

Author affiliation: Kyungpook National University

2020-09-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/75929

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/