Qualgebras and knotted 3-valent graphs
Abstract
This paper is devoted to qualgebras and squandles, which are quandles enriched with a compatible binary/unary operation. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. Topologically, qualgebras emerge as an algebraic counterpart of knotted 3-valent graphs, just like quandles can be seen as an "algebraization" of knots; squandles in turn simplify the qualgebra algebraization of graphs. Knotted 3-valent graph invariants are constructed by counting qualgebra/squandle colorings of graph diagrams, and are further enhanced using qualgebra/squandle 2-cocycles. Some algebraic properties and the beginning of a cohomology theory are given for both structures. A classification of size 4 qualgebras/squandles is presented, and their second cohomology groups are completely described.
Cite
@article{arxiv.1402.6673,
title = {Qualgebras and knotted 3-valent graphs},
author = {Victoria Lebed},
journal= {arXiv preprint arXiv:1402.6673},
year = {2014}
}