2025/04/13 by В. Г. Бардаков, Bardakov, V. G., D. A. Fedoseev +1
Computer Science · #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2504.09718
openalex publication_date 2025/04/13 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
A G-family of quandles is an algebraic construction which was proposed by A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro in 2013. The axioms of these algebraic systems were motivated by handlebody-knot theory. In the present work we investigate possible constructions which generalise G-family of quandles and other similar constructions (for example, Q- and (G,*,f)-families of quandles). We provide the necessary conditions under which the resulting object (called an (X,G,*g,f,⊗,⊕)-system) gives a colouring invariant of knotted handlebodies. We also discuss several other modifications of the proposed construction, providing invariants of spatial graphs with an arbitrary (finite) set of values of vertex valency. Besides, we consider several examples which in particular showcase the differences between spatial trivalent graph and handlebody-link theories.