Numerical irreducibility criteria for handlebody links

Abstract

In this paper we define a set of numerical criteria for a handlebody link to be irreducible. It provides an effective, easy-to-implement method to determine the irreducibility of handlebody links; particularly, it recognizes the irreducibility of all handlebody knots in the Ishii-Kishimoto-Moriuchi-Suzuki knot table and most handlebody links in the Bellettini-Paolini-Paolini-Wang link table.