Abstract: The handlebody-knot theory is a generalization of the classical knot theory and is a ‘quotient’ of the theory of spatial 3-valent graphs by so called IH-move. We discuss some known invariants for handlebody- knots and spatial graphs. In particular, we recall a G-family of quandles that 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 and give a possibili- ty to define some invariants. In the present work we investigate possible constructions which generalise G-family of quandles and other similar constructions. We provide the necessary conditions under which the resulting algebraic system gives a colouring invariant of handlebody- knots.

Cite: Бардаков В.Г.
Handlebody-links and spatial graphs
10th Russian-Chinese Conference on Knot Theory and Related Topics 30 сент. - 4 окт. 2024